Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer 1

Answer:

Step-by-step explanation:

Hello, we know that if the equation is

   $y=a(x-h)^2+k$

Then the vertex is the the point (h,k)

Here, the vertex is the point (-2,-20) so we can write, a being a real number that we will have to find,

$y=a(x-(-2))^2-20=a(x+2)^2-20$

On the other hand, we know that the y-intercept is (0,-12) so we can write

$-20=a(0+2)^2-12=4a-12\\\\\text{We add 12 and we divide by 4.}\\\\4a = -20+12=-8\\\\a = \dfrac{-8}{4}=-2$

So the equation becomes.

$\boxed{y=-2(x+2)^2-12}$

And we can give the standard form as below.

$y=-2(x+2)^2-12=-2(x^2+4x+4)-12\\\\=-2x^2-8x-8-12 \ \\\\\boxed{y=-2x^2-8x-20}$

Thank you.