Two functions are shown in the table below:
f(x) = −x^2 + 4x + 12
g(x) = x + 8
complete the table, then select the value that is a solution to f(x) = g(x).
a) x = 3
b) x = 4
c) x = 5
d) x = 6

Simply plug in the value of x.

f(x) = -x² + 4x + 12
f(3) = -(3²) + 4(3) + 12 = -9 + 12 + 12 = -9 + 24 = 15
f(4) = -(4²) + 4(4) + 12 = -16 + 16 + 12 = 0 + 12 = 12
f(5) = -(5²) + 4(5) + 12 = -25 + 20 + 12 = -25 + 32 = 7
f(6) = -(6²) + 4(6) + 12 = -36 + 24 + 12 = -36 + 36 = 0

g(x) = x + 8
g(3) = 3 + 8 = 11
g(4) = 4 + 8 = 12
g(5) = 5 + 8 = 13
g(6) = 6 + 8 = 14

f(x) = g(x) when x = 4.
f(4) = g(4) 
12 = 12