Question

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

Answer is:
c. y=(x-2)^2

Answer 1

`y=(x+2)^2`

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`

Answer 2

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