Question

Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 2 Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points) Group of answer choices x = 2 x = 3 x = 5 x = 6

Answer 1

First, we need to set up the equation f(x) = g(x) and then solve for x:
f(x) = g(x)
-x^2 + 4x + 12 = x + 2
-x^2 + 3x + 10 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-3 ± sqrt(3^2 - 4(-1)(10))) / 2(-1)
x = (-3 ± sqrt(49)) / -2
x = (-3 + 7) / -2 or x = (-3 - 7) / -2
x = -2 or x = 5
Therefore, the value that is a solution to f(x) = g(x) is x = 5.