Question

Which equation has a graph that is a parabola with a vertex at (-2,0)

Answer 1

The equation of a parabola with a vertex at (h,k) is
f(x)=a(x-h)+k
where a is a constant not equal to zero.
So for (h,k)=(-2,0), the general equation is
y=f(x)=a(x--2)^2+0,

y=a(x+2)^2, or
If a=1 and expand,
y=x^2+4x+4

Answer 2

The required equation of the parabola : y = x² + 4 + 4x

Explanation:

The vertex of the parabola is given to be : (-2 , 0)

The equation of a parabola with a vertex at (h , k) is : f(x) = a(x - h)² + k , where a is a constant not equal to zero.

Now, Vertex : ( h , k) = (-2 , 0)

So, h = -2 and k = 0

⇒ f(x) = a(x + 2)² + 0

⇒ y = a(x + 2)²

Take a = 1

⇒ y = x² + 4 + 4x

This is the required equation of the parabola.