Question

determine the x - intercepts of the following equation. ((x + 1)(-x + 3)=y) answer ((0,-3)) ((3,0)) ((0,3)) ((-1,0)) and ((-3,0)) ((0,-1)) and ((0,3)) ((-1,0)) and ((3,0))

Explanation:

Step1: Recall x - intercept definition

At x - intercepts, $y = 0$. So we set $(x + 1)(-x + 3)=0$.

Step2: Use zero - product property

If $ab = 0$, then either $a = 0$ or $b = 0$. Let $a=x + 1$ and $b=-x + 3$.
If $x+1 = 0$, then $x=-1$.
If $-x + 3=0$, then $x = 3$.
The x - intercepts are points of the form $(x,0)$. So the x - intercepts are $(-1,0)$ and $(3,0)$.

Answer:

$(-1,0)$ and $(3,0)$