Question

Two functions are shown in the table below f(x) equals -X squared plus 4X +12 And G(x)

equals X +2

Answer 1

`x = -2; x = 5`

Explanation:

Given

`f(x) = -x^2 + 4x + 12`

`g(x) = x +2`

Required

For what value of x is:
`f(x) = g(x)`

`f(x) = g(x)` implies that

`-x^2 + 4x + 12 = x + 2`

Collect like terms

`-x^2 + 4x -x + 12 -2 = 0`

`-x^2 + 3x + 10 = 0`

Expand

`-x^2 + 5x-2x + 10 = 0`

Factorize

`-x(x - 5)-2(x - 5) = 0`

Factor out x - 5

`(-x - 2)(x - 5) = 0`

Solve for x

`-x - 2 = 0; x - 5 = 0`

So:

`x = -2; x = 5`