Question

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

The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12).
The equation of the parabola is y =
x2 +
x +
.

Answer 1

this is wrong it needs to be 2 positives

Explanation:

Answer 2

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 = (-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.