1. The figure shows a graph of the function of f(x) in the xy-coordinate plane, with the vertex at (1,9) and the zeros
at -2 and 4.
x
5 6 7 8 9
The function g is defined by g(x) = -3x + 2. Which statements are true? Select ALL that apply.
f{-2) is greater than g(-2).
f{-1) is less than g(-1).
f{0) is greater than g(0)
f(1) is less than g(1).
f(2) is greater than g(2).

Answer:

f{0) is greater than g(0) and f(2) is greater than g(2).

Step-by-step explanation:

f{0) is greater than g(0) = f(0)=8  and g(0)=2

f(2) is greater than g(2) = f(2)=8 and g(2)= -4

The two statements that are correct are f(0) is greater than g(0), and f(2) is greater than g(2).

The general equation of a parabola is given as,

[tex]y=a(x-h)^2+k[/tex]

where (h,k) is the coordinate of the vertex of the parabola.

The equation of the parabola with vertex (1,9) can be written as,

[tex]y=a(x-h)^2+k\\\\y=a(x-1)^2+9[/tex]

Now, the value of a can be found by putting one zero of the parabola,

[tex]y=a(4-1)^2+9\\\\0=a(3)^2+9\\\\-9=a(3)^2\\\\-9=a9\\\\a=-1[/tex]

Thus, the equation of the parabola can be written as y=-(x-1)²+9.

A.) The value of the two functions when the value of x is -2 can be written as,

[tex]f(x)=-(x-1)^2+9\\\\f(-2)=-(-2-1)^2+9\\\\f(-2)=0[/tex]

[tex]g(x) = -3x + 2\\\\g(-2) = -3(-2) + 2\\\\g(-2)=8[/tex]

Therefore, f(-2) is less than g(-2).

B.) The value of the two functions when the value of x is -1 can be written as,

[tex]f(x)=-(x-1)^2+9\\\\f(-1)=-(-1-1)^2+9\\\\f(-2)=5[/tex]

[tex]g(x) = -3x + 2\\\\g(-1) = -3(-1) + 2\\\\g(-1)=5[/tex]

Therefore, f(-1) is equal to g(-1).

C.) The value of the two functions when the value of x is 0 can be written as,

[tex]f(x)=-(x-1)^2+9\\\\f(0)=-(0-1)^2+9\\\\f(0)=8[/tex]

[tex]g(x) = -3x + 2\\\\g(0) = -3(0) + 2\\\\g(0)=2[/tex]

Therefore, f(0) is greater than g(0).

D.) The value of the two functions when the value of x is 1 can be written as,

[tex]f(x)=-(x-1)^2+9\\\\f(1)=-(1-1)^2+9\\\\f(1)=9[/tex]

[tex]g(x) = -3x + 2\\\\g(1) = -3(1) + 2\\\\g(1)=1[/tex]

Therefore, f(1) is greater than g(1).

E.) The value of the two functions when the value of x is 2 can be written as,

[tex]f(x)=-(x-1)^2+9\\\\f(2)=-(2-1)^2+9\\\\f(2)=8[/tex]

[tex]g(x) = -3x + 2\\\\g(2) = -3(2) + 2\\\\g(2)=-4[/tex]

Therefore, f(2) is greater than g(2).

Thus, the two statements that are correct are f(0) is greater than g(0), and f(2) is greater than g(2).

Learn more about Equation of Parabola:

https://brainly.com/question/4074088

joanne cannot decide which of two washing machines to buy. The selling price of each is ​$660. The first is marked down by ​40%. The second is marked down by ​30% with an additional 10​% off. Find the sale price of each washing machine. Use pencil and paper. Explain why joanne should buy the first washing machine rather than the second if the machines are the same except for the selling price.

Natalia went to the mall and bought a pair of sneakers at a 30% off sale. The sneaker originally cost $120. How much did Natalia pay for the sneakers?

A.
B.
C.
D.
Whats the answer

What’s the area of this figure?

When a number is decreased by 7.5%, the result is 61. What is the original number to the nearest tenth?

A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter.

A store sells 50-pound bags of grass seed. one pound of grass seed covers about 400 square feet of field.

How many square feet does each 50-pound bag cover?

EXPERT HELP: DON'T GUESS and SHOW YOU WORK

An elevator will hold 780 kilograms. If each person weighs 60,000 grams, how many people will the elevator hold?

12 people
13 people
14 people
15 people

The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle?

5
10
25

Clare estimates that her brother is 4 feet tall. When they get measured at the doctor’s office, her brother’s height is 4 feet, 2 inches.

1. Should Clare's or the doctor's measurement be considered the actual height? Explain your reasoning.

2. What was the error, expressed in inches?

3. What was the error, expressed as a percentage of the actual height?

Need help please show work

PLEASE HELP!! IM TIMED!

Katherine was out at a restaurant for dinner when the bill came. Her dinner came to $34. She wanted to leave a 13% tip. How much was her meal plus the tip, before tax, in dollars and cents?

What would this look like as a equation

Three less than a variable

jo puts $4500 in a savings account that earns 5.5% interest. how much money will he have after 18 months?

help with this please free brainlist i promise only if you get it right though

A rectangular plate has an area of 30 1/16 square inches. If the width of the plate is 4 5/8 inches, what is its length in inches?

Help Please
Answer Choices
A- y = 2.5x
B- y = x + 10
C- y = -x + 10
D- y = -x + 60

PLEASE HELP!! SEE PICTURE BELLOW

Donna's kitchen is being re-tiled. The diagram of the kitchen is shown. What is the minimum number of square feet of tile that will be needed to complete this job?

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

please help me..for some reason its not letting me print out the question because it says *dont use such phrases* but anyways

can somebody plz help for brainliest

Pythagorean Theorem: [tex]a^{2}[/tex]+ [tex]b^{2}[/tex]= [tex]c^{2}[/tex]Question 8 options:
[tex]\sqrt{26}[/tex]

[tex]\sqrt{89}[/tex]
8
5

At the start of 6th grade, Maya measured 140 cm tall. At the start of 7th grade, Maya was 150.5 cm tall. What is the percent increase in Maya's height between the start of 6th and 7th grade?

geometry, I need help thanks

Please help I will reward brainliest

Please help I'm not the best at word problems and I really need help​

please give me the correct answer if you get it right ill give you brainiest if you don't know the answer leave

If x = 6 units, y = 6 units, and h = 8 units, find the area of the trapezoid shown above using decomposition.

A.
96 square units
B.
72 square units
C.
144 square units
D.
48 square units