Question

Two functions are shown in the table below.

Function - 1,2,3,4,5,6

f(x) = −x2 + 4x + 12
g(x) = x + 8
Complete the table on your own paper, then select the value that is a solution to f(x) = g(x).

x = 6
x = 3
x = 5
x = 4

Answer 1

`(d)\ x = 4`

Explanation:

Given

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

`g(x) = x + 8`

Required

Find x such that:
`f(x) = g(x)`

This gives:

`-x^2 + 4x + 12 = x+8`

Collect like terms

`-x^2 + 4x -x + 12 -8=0`

`-x^2 + 3x +4 =0`

Expand

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

Factorize

`x(x - 4) - 1(x-4) = 0`

Factor out x - 1

`(x- 1)(x - 4)=0`

Solve:

`x =1\ or\ x = 4`