Question

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

Answer 1

Answer:

The vertex of a quadratic equation corresponds to the point where the maximum or minimum value is located.

If the function has a positive leading coefficient, the vertex corresponds to the minimum value.

If it has a negative leading coefficient,  the vertex corresponds to the maximum valuevalue

If the vertex is located at

(–2, 0)

The possibilities are

y =  (x-2)^2

or,

y = - (x-2)^2

Since the problem tells us the answer, we adopt the positive values

Answer:

y =  (x-2)^2

See attached picture

Answer 2

Answer:

$y=(x+2)^2$

Step-by-step explanation:

A graph that is a parabola with a vertex at (–2, 0)

Vertex form of parabola equation is

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

where (h,k) is the vertex

WE are given with vertex (-2,0)

(-2,0) is (h,k)

h=-2 and k=0

Plug the value in vertex form of equation. Lets take a=1

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

Equation becomes $y=1(x-(-2))^2 + 0$

$y=(x+2)^2$