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).
O x = 2
Ox= 3
O x = 5
O x = 6

Answer 1

C. x=5

Explanation:

Please see attachments. You'll see that at the x=5 y will equal 7.

Hope this helps!

Answer 2

The correct option is x = 5

Please find the attached graph of the function

Explanation:

The given functions are;

1) f(x) = -x² + 4·x + 12

2) g(x) = x + 2

The table of values are therefore;

x, f(x), g(x)

-7, -65, -5

-6, -48, -4

-5, -33, -3

-4, -20, -2

-3, -9, -1

-2, 0, 0

-1, 7, 1

0, 12, 2

1, 15, 3

2, 16, 4

3, 15, 5

4, 12, 6

5, 7, 7

6, 0, 8

Therefore the solution to the equation f(x) = g(x), occurs at x = -2 and x = 5, where f(x) = g(x) = 0 and 7 respectively

To verify, we have;

Equating the two functions gives;

f(x) = g(x)

-x² + 4·x + 12 = x + 2

-x² + 4·x + 12 - (x + 2) = 0

-x² + 3·x + 10 = 0

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

x = 5 or -2

The correct option is x = 5.