Question

PLEASE ANSWER ASAP!!

Answer 1

Answer:  Choice A

f(x) = (x + 2)^2 - 11

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Work Shown:

y = x^2 + 4x - 7

y+7 = x^2 + 4x

y+7+4 = x^2 + 4x + 4

y+11 = x^2 + 4x + 4

y+11 = (x + 2)^2

y = (x + 2)^2 - 11

f(x) = (x + 2)^2 - 11

In the third step, I added 4 to both sides to complete the square for the x^2+4x portion. Notice that (x+2)^2 = x^2+4x+4. So I added 4 to fill in the missing piece needed to complete the square.

Put another way the '4' added to both sides is because we first divided the x coefficient 4 in half to get 4/2 = 2. Then you square it to get 2^2 = 4.

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Alternative Method (optional)

y = x^2 + 4x - 7 is in the form of y = ax^2+bx+c

where: a = 1, b = 4, c = -7

Plug those a,b values into the formula below

h = -b/(2a)

h = -4/(2(1))

h = -2

This is the x coordinate of the vertex.

Use it to find the y coordinate of the vertex.

y = x^2 + 4x - 7

y = (-2)^2 + 4(-2) - 7

y = -11

The vertex is located at (h,k) = (-2,-11)

We have the template y = a(x-h)^2 + k update to y = (x + 2)^2 - 11 after plugging in a = 1, h = -2, and k = -11.

Answer 2

Give them brainiest ^^^^ (: