Question

Write a function in any form that would match the graph shown below

Answer 1

Answers:

• Vertex form:  y = -2(x-1)^2 + 8
• Standard form: y = -2x^2 + 4x + 6

Pick whichever form you prefer.

=============================================================

Explanation:

The vertex is the highest point in this case, which is located at (1,8).

In general, the vertex is (h,k). So we have h = 1 and k = 8.

One root of this parabola is (-1,0). So we'll plug x = -1 and y = 0 in as well. As an alternative, you can go for (x,y) = (3,0) instead.

Plug those four values mentioned into the equation below. Solve for 'a'.

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

0 = a(-1-1)^2+8

0 = a(-2)^2+8

0 = 4a+8

4a+8 = 0

4a = -8

a = -8/4

a = -2

The vertex form of this parabola is   y = -2(x-1)^2+8

Expanding that out gets us the following

y = -2(x-1)^2+8

y = -2(x^2-2x+1)+8

y = -2x^2+4x-2+8

y = -2x^2+4x+6 .... equation in standard form