Write the equation in vertex form for the graph below.

Question

asked Mar 16, 2021 83.4k views

2 Answers

Dhara Parmar · Answer 1 · 2021-03-21T15:16:52+0000

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