Question

1. for the functions ( y = (x - r)(x - s) ) graphed below, give values for the x-intercepts ( r ) and ( s ), and write formulas for the functions in factored form.

(a)
(b)
(c)

part	( r, s ) ( ( r ) is the smallest one)	formula ( y = (x - r)(x - s) )
(b)
(c)

Explanation:

Step1: Identify intercepts for (a)

The x-intercepts are $x=1$ and $x=3$. Since $r$ is smaller, $r=1$, $s=3$.
Substitute into $y=(x-r)(x-s)$:
$y=(x-1)(x-3)$

Step2: Identify intercepts for (b)

The x-intercepts are $x=-2$ and $x=4$. Since $r$ is smaller, $r=-2$, $s=4$.
Substitute into $y=(x-r)(x-s)$:
$y=(x-(-2))(x-4)=(x+2)(x-4)$

Step3: Identify intercepts for (c)

The x-intercepts are $x=-5$ and $x=0$. Since $r$ is smaller, $r=-5$, $s=0$.
Substitute into $y=(x-r)(x-s)$:
$y=(x-(-5))(x-0)=(x+5)x$

Answer:

Part	r, s (r is the smallest one)	Formula $y=(x-r)(x-s)$
(b)	$r=-2, s=4$	$y=(x+2)(x-4)$
(c)	$r=-5, s=0$	$y=x(x+5)$