Question

What is the vertex form of # f(x) = -2x^2+3x+12 #?

Answer 1

`f(x) = -2(x - 3/4)^2 + 105/8`

Explanation:

First, find x-coordinate of vertex:
`x = -b(2a) = -3/-4 = 3/4`
Next, find y-coordinate of vertex
`f(3/4) = -2(9/16) + 3(3/4) + 12 = -9/8 + 9/4 + 12 = 105/8`
Vertex form:
`f(x) = - 2(x - 3/4)^2 + 105/8`