Question

Two functions are shown in the table below.

Answer 1

Answer:

$(d)\ x = 4$

Step-by-step 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:

$x =1\ or\ x = 4$