Question

Write the equation in vertex form for the graph below.

Answer 1

Given:

The graph of the parabola with vertex (-2,-4)

We need to determine the equation of the parabola in vertex form.

Equation in vertex form:

The general form of the equation of the parabola in vertex form is given by

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

where a is the constant and (h,k) is the vertex.

Substituting the vertex (-2,-4) in the above formula, we get;

$y=a(x+2)^2-4$  -------- (1)

To determine the value of a, let us substitute the point that the parabola passes through.

Hence, substituting the point (0,8) in equation (1), we get;

$8=a(0+2)^2-4$

$8=a(2)^2-4$

$8=4a-4$

$12=4a$

$3=a$

Thus, the value of a is 3.

Substituting the value a = 3 in equation (1), we get;

$y=3(x+2)^2-4$

Thus, the equation of the parabola in vertex form is $y=3(x+2)^2-4$