The roots have positive or same signs when c>0.
Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.
[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]
Roots of quadrant equation have Samsame sign if product of roots >0.
[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]
Roots of quadratic equation have positive sign if product of roots<0.
c>0.
Combining results, we get:-
roots have positive signs when:-
c>0.
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Select all the conclusions you can draw if you know that <1 is congruent to <8?
Knowing that <1 is congruent to <8 allows us to draw the following conclusions: The angles <1 and <8 have the same measure. They are alternate interior angles formed by a transversal intersecting two parallel lines. If <1 is part of a triangle or polygon, then <8 is also part of that same triangle or polygon.
What is Polygon?
In geometry, a polygon is a two-dimensional shape that is made up of straight lines. It is a closed figure with three or more line segments that connect at their endpoints to form a closed shape.
Polygons can have any number of sides, but they must have at least three sides. Some examples of polygons include triangles, rectangles, squares, pentagons, hexagons, and so on.
The properties of a polygon, such as its angles and sides, can be calculated and analyzed using mathematical formulas and principles. Polygons are commonly used in geometry, architecture, engineering, and many other fields.
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What is the area of a triangle with a base of 5x - 4 and a height of 2x +6?
The area of the triangle is 5x² + 11x -12 whose base is 5x - 4 and height is 2x + 6.
What is triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.
According to question:The formula for calculating a triangle's area is:
Area = 1/2 x Base x Height
Plugging in the given values, we get:
Area = 1/2 x (5x - 4) x (2x + 6)
Simplifying, we get:
Area = 1/2 x (10x² + 22x - 24)
Distributing the 1/2, we get:
Area = 5x² + 11x - 12
Therefore, the area of the triangle is 5x² + 11x - 12.
The three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.
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A 40-year-old person who wants to retire at age 60 starts a yearty retirement contribution in the amount of $6,000. The retirement account is forecasted to average a 5% annual
rate of retum, ylelding a total balance of $198,395.72 at retirement age.
If this person had started with the same yearty contribution at age 30, what would the difference be in the account balances?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
O $200,732.63
O $200,237.36
O $398,633.09
O S389.633.90
Para calcular la diferencia en los saldos de la cuenta de jubilación, necesitamos calcular los saldos en ambos casos y luego restarlos.
Para el primer caso, donde la persona comienza a hacer contribuciones anuales a los 40 años, tenemos:
Número de años hasta la jubilación: 60 - 40 = 20 años
Contribución anual: $6,000
Tasa de interés anual: 5%
Usando la fórmula para el valor futuro de una serie de pagos (anualidades) ordinarias, tenemos:
VF = Pmt x [(1 + r)^n - 1] / r
Donde VF es el valor futuro (saldo de la cuenta), Pmt es la contribución anual, r es la tasa de interés anual y n es el número de períodos (en este caso, el número de años hasta la jubilación).
Entonces, para este caso, el saldo de la cuenta sería:
VF = $6,000 x [(1 + 0.05)^20 - 1] / 0.05 = $198,395.72
Para el segundo caso, donde la persona comienza a hacer contribuciones anuales a los 30 años, tenemos:
Número de años hasta la jubilación: 60 - 30 = 30 años
Contribución anual: $6,000
Tasa de interés anual: 5%
Usando la misma fórmula que antes, el saldo de la cuenta sería:
VF = $6,000 x [(1 + 0.05)^30 - 1] / 0.05 = $398,633.09
Entonces, la diferencia en los saldos de la cuenta sería:
$398,633.09 - $198,395.72 = $200,237.37
Por lo tanto, la respuesta es la opción B) $200,237.36.
Answer: B- $200,237.36
Step-by-step explanation: Got it right on the test! And also the person above helped me out a lot!!
a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water. find a) the rotational speed at which the water just touches the bottom of the cylinder and b) the resulting pressure at points a and b.
a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water.
a) Rotational speed at which the water just touches the bottom of the cylinder:
We will use the formula for centripetal force for a liquid with the volume of a cylinder to obtain the rotational speed at which the water just touches the bottom of the cylinder.
The formula for centripetal force for a liquid with the volume of a cylinder is as follows:
F = (ρr²πh)ω²WhereF:
Centripetal forceρ: Densityr: Radiush : Heightω: Rotational speed Substituting the given values,
we get: F = (1000 kg/m³ × (0.1m)² × π × 0.12m)ω²F
= 377 Nω
= √(F/m)ω
= √(377 N/ 10 kg)ω
= √37.7ω = 6.14 rad/sb)
Pressure at points A and B:
We will use the formula for hydrostatic pressure for a liquid to calculate the pressure at points A and B. The formula for hydrostatic pressure for a liquid is as follows:
P = ρgh
Where,
P: Pressureρ: Densityg: Acceleration due to gravity: DepthSubstituting the given values for point A,
we get P = 1000 kg/m³ × 9.8 m/s² × 0.1 mP
= 980 Pa
Substituting the given values for point B,
we get P = 1000 kg/m³ × 9.8 m/s² × 0.22 mP
= 2156 Pa
The resulting pressure at point A is 980 Pa and the resulting pressure at point B is 2156 Pa.
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help me please........................................................
Answer:
To find the area of the given figure, we can divide it into two separate shapes, a rectangle and a triangle, and then add their areas together.
First, we can find the area of the rectangle by multiplying its length and width. From the diagram, we can see that the length of the rectangle is 12 cm and the width is 5 cm.
Area of rectangle = length x width
Area of rectangle = 12 cm x 5 cm
Area of rectangle = 60 cm^2
Next, we can find the area of the triangle by using the formula for the area of a triangle, which is:
Area of triangle = 1/2 x base x height
From the diagram, we can see that the base of the triangle is 5 cm and the height is 8 cm.
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 5 cm x 8 cm
Area of triangle = 20 cm^2
Finally, we can find the total area of the figure by adding the area of the rectangle and the area of the triangle:
Total area = area of rectangle + area of triangle
Total area = 60 cm^2 + 20 cm^2
Total area = 80 cm^2
Therefore, the area of the given figure is 80 square centimeters.
Step-by-step explanation:
Scott has a blueprint of the new deck he is building with dimensions 7.5 inches by 4.5 inches. the actual deck will have dimensions 20 feet by 12 feet. what is the scale?
The scale factor of the blueprint of the deck is 1.5 inches = 4 feet
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, Scott has a blueprint of the new deck he is building with dimensions 7.5 inches by 4.5 inches. The actual deck will have dimensions 20 feet by 12 feet.
We need to find the scale factor,
7.5 / 20 = 1.5 / 4
Therefore,
There are 1.5 inches in 4 feet
Hence, the scale factor of the blueprint of the deck is 1.5 inches = 4 feet
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Answer:
hi
Step-by-step explanation:
guvuvugjdhddiebeidgddb
The following set of scores was obtained from a quiz: 4, 5, 8,9, 11, 13, 15, 18, 18, 18, 20. The teacher computes the usual descriptive measures of central tendency and spread for these data and then discovers that an error was made. One of the 18s should have been a 16. Which of the following measures will NOT need to be changed from the original computations? (There may be more than one correct answer.) Mean 73 Median Standard deviation 1 IQR They all will need to be changed.
All of the measures of central tendency and spread for these data will need to be changed from the original computations in order to reflect the correct values.
In this case, the initial set of scores was 4, 5, 8, 9, 11, 13, 15, 18, 18, 18, and 20. The teacher initially computed the mean, median, standard deviation, and IQR and then discovered that one of the 18s should have been a 16.The mean is affected by any change in the data, so this measure will need to be changed to reflect the correct values. The new mean is 73.The median is also affected by any change in the data, so this measure must be recalculated to reflect the correct values.
The new median is 15.5.The standard deviation measures the spread of data from the mean, so this measure must also be changed to reflect the correct values. The new standard deviation is 1.4.Finally, the IQR measures the spread of the middle 50% of the data, so this measure must also be changed to reflect the correct values. The new IQR is 6. All of the measures of central tendency will need to be changed.
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The sales of books at a local book fair are shown in the histogram.
A histogram titled Book Sales with the x-axis labeled Number of Books. The x-axis has intervals of 0 to 1, 2 to 3, 4 to 5, 6 to 7, 8 to 9 and 10 to 11. The y-axis is labeled Frequency and starts at 0 with tick marks every two units up to 10. There is a shaded bar above 1 to 3 that stops at 3, above 2 to 3 that stops at 4, above 5 to 6 that stops at 8, above 6 to 7 that stops at 2, above 8 to 9 that stops at 4 and above 10 to 11 that stops at 8.
Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 11. This might be because the book fair offers fair prices, so most costumers bought books.
The data is skewed, with a maximum range of 14. This might be because many of the customers wanted to stock up before the winter.
The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.
The data is symmetric with a maximum range of 10. This might mean that most customers bought less than 3 books because that is all that they could carry.
"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter."
What is a histogram?A histogram is a type of graph used in statistics to represent the distribution of a set of continuous data. It consists of a set of adjacent bars, where the area of each bar represents the frequency or relative frequency of observations within a specific interval or "bin" of the data.
The x-axis of a histogram shows the range of values for the variable being measured, divided into intervals or bins. The y-axis shows the frequency or relative frequency of observations within each interval or bin. Histograms are commonly used to show the shape, center, and spread of a distribution of data, as well as any potential outliers or gaps in the data.
In the given question, the histogram shows a skewed distribution, where the majority of book sales occurred in the lower intervals (1-3, 2-3, and 5-6) and the frequency decreases as the number of books sold increases. The maximum range of the data is 14 (from the interval 10-11 to the interval 2-3), which suggests a wide spread of book sales across different intervals.
"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter." comes the closest to describing the spread and distribution of the data shown in the histogram.
The other options do not accurately describe the shape or spread of the data shown in the histogram.
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Answer:
C: The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.
Step-by-step explanation:
What is the largest number less than 570 that is divisible by 9?
(I need it for a assignment on Beast Academy)
Answer:
567 is the correct number.
Step-by-step explanation:
[tex]5 + 6 + 7 = 18[/tex]
[tex]1 + 8 = 9[/tex]
So 567 is divisible by 9 since
[tex]567 \div 9 = 63[/tex]
What is the rage of the function represented by the graph?
The range of the function represented by the graph is (-3, 0). This means that the output (or y-value) can range from -3 to 0 for any given input (or x-value).
What is function?A function is a block of code that has been written to perform a specific task. It can accept input, perform operations on that input, and return a result. Functions are an essential part of coding, as they allow for code to be reused, and make programs easier to read and debug. Functions can be used in almost any programming language, and are often used to perform calculations, display information, and handle user input. Reusable functions can help to reduce the amount of code needed to accomplish a task, making programs easier to maintain and update.
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There are 12 red roses 5 yellow roses and 3 white rises in a vase felix takes a rose at random from the vase what is the probability that he takes a white rose?
Answer: 8/20
Step-by-step explanation:
Can someone help me with this math problem pls! #Percents
Answer: $3.64
Step-by-step explanation:
At the store, you buy four toys for $1.5, which means you pay $1.5 * 4, or $6.
Then, you calculate the sales tax, which is 6%, which means you multiply $6 by (100% + 6%), or $6*(1.06) which is $6.36.
Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.
C = {[1 2 3], ['cell '; 'array'], 24; [3; 6; 9], [22, 44; 66, 88], 'matrix'} what is the result of c{2, 1}?
'cell '. The element in the second row and first column of the cell array C is accessed using the phrase c(2,1). The first element in the second row of C is the string "cell," which is that element.
The element in the second row and first column of the cell array C is accessible by the equation c(2,1). The first element in the second row of C is the string "cell," which makes up that element. The string "cell" is the result of c(2,1).
The curly braces in MATLAB are used to retrieve the contents of a cell array. "Access the contents of the cell in the second row and first column of C" is what the phrase C2,1 implies. The string in question is the outcome of the expression since it is present in the relevant cell.
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What’s is the answer to this
Answer:
What is the measure of angle F?
B. 65Step-by-step explanation:
You're welcome.
y=-x+2
please anwser quickly as you can
Answer: -2.0
Step-by-step explanation:
match the following. 1. a length equal to the height in a square 2. any rhombus can be created by rotating this shape around the midpoint of its base 3. found by dividing 360 by the number of sides of a regular polygon 4. height of a parallelogram 5. each angle in a rectangle 6. a special type of trapezoid 7. perpendicular distance from the center of a regular polygon to its side 8. a special type of regular polygon
Altitude
base
apothem
parallelogram
isosceles triangle
right angle central angle
The following points are matched:
A length equal to the height in a square - baseAny rhombus can be created by rotating this shape around the midpoint of its base - right angle (square)Found by dividing 360 by the number of sides of a regular polygon - central angleHeight of a parallelogram - altitudeEach angle in a rectangle - right angleA special type of trapezoid - parallelogramThe perpendicular distance from the center of a regular polygon to its side - apothemA special type of regular polygon - equilateral triangleAll sides of a square are equal.On rotating a square around the midpoint of its base, a rhombus is created. This happens due to the right angles between the sides of the square.The central angle of a regular polygon is obtained by dividing 360 by the number of sides of the same polygon.The altitude of a parallelogram is defined as its height.By the property of a rectangle, it has only right angles.A trapezoid is a quadrilateral with at least one pair of parallel sides while a parallelogram has both pairs of parallel sides.The apothem is the perpendicular distance from the center of a regular polygon to its side.An equilateral triangle is a special type of regular polygon with three equal sides and three equal angles.Thus, the definitions are matched to their respective terms.
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Solve for x. using the tangent lines.
50 deg
X
x =[?]^
This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.
What is tangent?Tangent is a line or plane that touches a curve or surface at a single point. It is a measure of the steepness of a curve or surface at a particular point. It is equal to the ratio of the change in the y-coordinate to the change in the x-coordinate of a point on the curve. Tangent is used in many areas of mathematics and physics, including calculus, geometry, and mechanics. It is also used to describe the rate of change in a function, as well as to define the angle between two intersecting lines.
The tangent line equation for a line with a slope of 50 degrees is y = tan(50°)x.
To solve for x, you must rearrange the equation to isolate x on one side of the equation.
To do this, divide both sides of the equation by tan(50°), giving the equation x = y/tan(50°). This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.
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Given the right triangle below, what is the measure of angle E
The angle E is 50.21°
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
Given, the right angle triangle at ∠F = 90°
According to the figure, base = 16cm, hypotenuse = 25cm
Apply Cosine rule;
Cos x = 16/25
x = Cos⁻¹ (16/25)
x = 50.21°
Therefore, the angle E is 50.21°
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Triangle: According to the question the measure of angle E is 50.21°
What is a triangle?A triangle is a three-sided polygon which has three angles and three vertices. It is one of the basic shapes in geometry and is a fundamental shape in many mathematical and engineering fields. A triangle can be classified according to its angles or sides. Right triangles have one angle that is a right angle (90°) and two acute angles, obtuse triangles have one obtuse angle (greater than 90°) and two acute angles, and equilateral triangles have three equal angles and three equal sides.
Given, the right angle triangle at ∠F = 90°
According to the figure, base = 16cm, hypotenuse = 25cm
Apply Cosine rule;
Cos x = 16/25
x = Cos⁻¹ (16/25)
x = 50.21°
Therefore, the angle E is 50.21°
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When comparing the z-scores of values from different data sets, how do I know which one is "better"?
Higher z-scores imply more severe or unusual observations in the data set since they are indicative of values that are further from the mean en terms of standard deviations.
Why do people utilize z-score?With the use of Z-scores, you are able to scale up data points from populations with various means and standard deviations. The comparison of observations for various sorts of variables, which would otherwise be challenging, is now possible thanks to the use of a common scale.
In plain terms, what is z-score?The relationship between a value and a group of values' mean is described statistically by the Z-score. Standard deviations from of the mean serve as the unit of measurement for Z-score. The score for a data point is equal to a mean score if the Z-score is 0.
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Let f(x)=x2−4. What is the average rate of change of f(x) from −5 to −2 ?
A. -1/7
B. 1/7
C. -7
D. 7
Answer:
Step-by-step explanation:
To find the average rate of change of the function f(x) from -5 to -2, we need to calculate:
(f(-2) - f(-5))/(-2 - (-5))
First, let's find f(-2) and f(-5):
f(-2) = (-2)^2 - 4 = 0
f(-5) = (-5)^2 - 4 = 21
Substituting these values in the above formula, we get:
(0 - 21)/(-2 + 5) = -21/3 = -7
Therefore, the average rate of change of f(x) from -5 to -2 is -7.
So the answer is (C) -7.
1. What is the value of Pi to four decimal places?
2. How many vertices are there on a cube?
3. What is the prime number closest to 100?
4. What is the sum of the internal angles of a hexagon?
5. Which number is represented in binary as 100?
The value of Pi to four decimal places is 3.1416.
There are 8 vertices on a cube.
The prime number closest to 100 is 97.
The sum of the internal angles of a hexagon is 720 degrees.
The number represented in binary as 100 is 4 in decimal notation.
Answer:
The value of Pi to four decimal places is 3.1416.There are eight vertices on a cube.The prime number closest to 100 is 97.The sum of the internal angles of a hexagon is 720 degrees.The number represented in binary as 100 is 4 in decimal form.After how many weeks do you think it would be unreasonable to continue counting individual mosquitoes? And finally, at the end of the 13-week mosquito season, how many mosquitoes would you expect to be in the trap? Use complete sentences to explain both of your answers below.
At the end of the 13-week mosquito season, we would expect to find around 558 mosquitoes in the trap.
It would be unreasonable to continue counting individual mosquitoes after about 13 weeks, since that is usually the end of the mosquito season. This is because, after the 13th week, the number of mosquitoes captured in the trap is likely to decrease significantly, making it pointless to count them individually. At the end of the 13-week mosquito season, the expected number of mosquitoes in the trap can be estimated using a simple exponential decay function.
Assuming the initial number of mosquitoes in the trap is N0 and the rate of decay is k, the number of mosquitoes after t weeks (Nt) can be calculated using the following equation: [tex]Nt = N0 * e-kt.[/tex]
For example, if the initial number of mosquitoes in the trap is 1000 and the rate of decay is 0.2, then the number of mosquitoes after 13 weeks can be estimated as follows:[tex]N13 = 1000 * e-0.2*13 = 558[/tex]
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A boat is heading towards a lighthouse, where Samantha is watching from a vertical
distance of 106 feet above the water. Samantha measures an angle of depression
to the boat (at point A) to be 18°. At some time later, Samantha takes another
measurement and finds the angle of depression to the point (now at point B) to be
69°. Find the distance from point A to point B.
Round your answer to the nearest foot.
Answer:326
Step-by-step explanation:
Increase 80g by 25%
Help me i’ll give you 15 points!
Answer:
To increase 80g by 25%, you need to find 25% of 80 and then add that to 80.
25% of 80 is (25/100) x 80 = 20
So, to increase 80g by 25%, you add 20g to 80g:
80g + 20g = 100g
Therefore, an increase of 25% on 80g is 100g.
Step-by-step explanation:
there were 90 runners to start a race. in the firdt half of the race, 1/6 of them dropped out. in the second half of the race, 1/3 of the remaining runners dropped out. how many runners finished the race?
Answer:
50
Step-by-step explanation:
1/6 of 90 is 15 (1/6x90/1 = 90/6 which equals 15)
then, subtract that from 90 to give you the amount of runners that left in the first half (90-15= 75)
then 1/3 of 75 is 25 (1/3x75/1= 75/3which equals 25)
and you subtract the runners that left from the total amount of runners (75-25=50)
Triangle ABC has coordinates A(4,1), B(5,9),and C (2,7). If the triangle is translated 7 units to left, what are the coordinates of B'?
Answer:
(-2,9)
Step-by-step explanation:
when moving it 5 units left on the x axis it would be 5-7
So in turn you would be given (-2,9)
Because the y stays the same you would still have (?,9)
A right triangle has a leg length of 24 yards and a hypotenuse of 45 yards. Find the length of the other leg
The length of the other leg is 38 yards
What is Right Triangle?Right Triangle is a triangle in which one of the interior angles measures 90 degrees. It is also a figure where one of the three angles measures 90° and the other two angles are acute that sums to 90°.
Using Pythagoras theorem to the Right Triangle,
C^2 = A^2 + B^2
Where C = Hypotenuse = 45 yards
A = One of the leg = 24 yards
To get the value of B,
C^2 = A^2 + B^2
B^2 = C^2 - A^2
B^2 = (45^2) - (24^2)
B^2 = 2025 - 576
B^2 = 1449
B = √1449
B = 38 yards
Therefore, the length of other leg is 38 yards
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7.2 L of water are poured into a container in the shape of a right rectangular prism. The inside of the container is 50 cm long, 20 cm wide, and 25 cm tall. How far from the top of the container is the surface of the water? (1 L = 1000 cm³)
Answer:
convert the l to volume Wich will give 7200 cm3 .
use the equation for volume which is V=L*B*H where you will replace B,L and leave out H since that's what we are looking for:
V=L*B*H
7200=50*20*H
7200=1000H
7200÷1000=H
therefore H of liquid is 7.2 cm ....to get the height from top subtract the height of liquid from that of a container which will give : 20-7.2= 12.8cm3
there the answer is 12.8
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whats 1+1-1
Answer:
1
Step-by-step explanation:
LOL
Answer:
1+1-1=1
Step-by-step explanation:
1+1=2
2-1=1
your answer is 1
Select the correct answer. Which graph represents this equation? A. The graph shows an upward parabola with vertex (minus 3, minus 4.5) and passes through (minus 7, 3.5), (minus 6, 0), (0, 0), and (1, 3.5) B. The graph shows an upward parabola with vertex (3, minus 4.5) and passes through (minus 1, 3.5), (0, 0), (6, 0), and (7, 3.5) C. The graph shows an upward parabola with vertex (minus 2, minus 6) and passes through (minus 5, 7), (minus 4, 0), (0, 0), and (1, 7) D. The graph shows an upward parabola with vertex (2, minus 6) and passes through (minus 1, 7), (0, 0), (4, 0), and (5, 7)
Answer:
A
Step-by-step explanation: