Question

what are the solutions for the system of equations? select all that apply.
$f(x) = (x - 4)^2 - 8$
$f(x) = -x + 2$
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$square$ (0,2) $square$ (1,1) $square$ (2,0) $square$ (4,-2) $square$ (6,-4)

Explanation:

Step1: Set equations equal

$$(x-4)^2 - 8 = -x + 2$$

Step2: Expand left side

$$x^2 - 8x + 16 - 8 = -x + 2$$

Step3: Simplify equation

$$x^2 - 7x + 6 = 0$$

Step4: Factor quadratic

$$(x-1)(x-6) = 0$$

Step5: Solve for x

$x=1$ or $x=6$

Step6: Find y for x=1

$$y = -1 + 2 = 1$$

Step7: Find y for x=6

$$y = -6 + 2 = -4$$

Answer:

(1,1), (6,-4)