Question

find all points of intersection between the graphs of the functions f(x)=(x + 5)(x - 4) and g(x)=x + 5.

Explanation:

Step1: Set f(x) equal to g(x)

$(x + 5)(x - 4)=x + 5$

Step2: Expand the left - hand side

$x^{2}-4x+5x - 20=x + 5$
$x^{2}+x - 20=x + 5$

Step3: Move all terms to one side

$x^{2}+x - 20-(x + 5)=0$
$x^{2}+x - 20 - x - 5=0$
$x^{2}-25 = 0$

Step4: Factor the quadratic equation

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

Step5: Solve for x

$x+5 = 0$ gives $x=-5$; $x - 5=0$ gives $x = 5$
When $x=-5$, $g(-5)=-5 + 5=0$, $f(-5)=(-5 + 5)(-5 - 4)=0$
When $x = 5$, $g(5)=5 + 5=10$, $f(5)=(5 + 5)(5 - 4)=10$

Answer:

The points of intersection are $(-5,0)$ and $(5,10)$