Question

1. $y=(x+4)(x-2)$

• identify the zeroes, and y-intercept then graph

zeroes (x-intercepts):
vertex: $(-1,-9)$
y-intercept:

Explanation:

Step1: Find zeros (x-intercepts)

Set $y=0$, solve $(x+4)(x-2)=0$.
$x+4=0 \implies x=-4$; $x-2=0 \implies x=2$

Step2: Calculate y-intercept

Set $x=0$, substitute into $y=(0+4)(0-2)$.
$y=(4)(-2)=-8$

Step3: Plot key points for graph

Plot zeros $(-4,0)$, $(2,0)$; vertex $(-1,-9)$; y-intercept $(0,-8)$, then draw a parabola through all points.

Answer:

Zeros (x-intercepts): $x=-4$ and $x=2$ (points $(-4, 0)$ and $(2, 0)$)
y-intercept: $y=-8$ (point $(0, -8)$)
The graph is a parabola passing through $(-4,0)$, $(0,-8)$, $(2,0)$, and vertex $(-1,-9)$.