Determine the Y intercept PLEASE HELP!! X Y -3 -3 0 -1 3 1

This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

creativ13 [48]

Answer:

Part a) The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

The equation of a vertical parabola written in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

$f(x)=a(x-2)^2-8$

Find the value of the coefficient a

take one point from the graph

(0,0)

substitute in the equation

$0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2$

therefore

The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

$f(x)=a(x-x_1)(x-x_2)$

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

so

$f(x)=a(x-0)(x-4)$

$f(x)=ax(x-4)$

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

$-8=a(2)(2-4)\\-8=-4a\\a=2$

therefore

The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

4 0

3 years ago

can someone please help with my geometry homework?? i haven't been in the class for a year and i'm starting off the second semes

sattari [20]

Ok so for number 5, AB is proportional to BC just like PQ is proportional to QR. AB = 9, BC = 15, PQ = 3, and QR = x. 9/15 = 3/x. Cross Multiply: This gives you - 9x = 45. Divide both sides by 9, and you get x = 5. QR = 5

3 0

2 years ago

True or false. -5+ ( -3 +( -8) = -5 + ( - 3 + 8 )

ivanzaharov [21]

False:

-5 + -3 + (-8) = -16

-5 + -3 + 8 = 0

hope this helps

8 0

3 years ago

Read 2 more answers

Do these ratios form a proportion? $42 per 33 customers $28 per 22 customers yes no

Iteru [2.4K]

No I have to have a denomination

8 0

3 years ago

Read 2 more answers

Can someone pls help ASAP :) I’ll give brainiest

Anna71 [15]

Answer:

D. (2x)(3x) + 5(3x - 2)

good luck, i hope this helps :)

5 0

3 years ago