Question

Two functions are shown in the table below.

Function: 1 2 3 4 5 6
f(x) = -x^2 + 4x+12

g(x) = -x + 6

Complete the table on your own paper, then select the value that is a solution to f(x) = g(x).

Answers:
A) x= 2
B) x=3
C) x=5
D) x=6

Answer 1

To find which x coordinate makes f(x) = g(x) or to find when those lines intersect, we need to set them equal:
`- {x}^(2) + 4x + 12 = - x + 6`

Add x-6 to both sides of the equation:
`- {x}^(2) + 5x + 6 = 0`

Make
`- {x}^(2)` positive by multiplying the equation by -1:
`{x}^(2) - 5x -6 = 0`

Now find the x using quadratic formula:
`x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac } }{2a}`

Plug the values:
`x = \frac{ - ( - 5)\pm \sqrt{ { (- 5)}^(2) - 4 * 1 * - 6 } }{2 * 1}`

Simplify:

`x = (5 \pm √(25 + 24) )/(2) = (5\pm √( 49) )/(2)`

Now we need to branch the plus-minus sign:

`x = (5 + 7)/(2) = (12)/(2) =6`

`x = (5 - 7)/(2) = ( - 2)/(2) = - 1`

Because -1 isn't in the choices, 6 is the right answer.