Question

question 5
3 pts
a parabola has x-intercepts of (-4,0) & (2,0) and goes through the point (0,-4). write the quadratic equation in factored form.
$\bigcirc y=-2(x + 4)(x - 2)$
$\bigcirc y=\frac{1}{2}(x + 4)(x - 2)$
$\bigcirc y=2(x + 2)(x - 4)$
$\bigcirc y=(x + 4)(x - 2)$

Explanation:

Step1: Recall factored form formula

For x-intercepts $x=r_1$ and $x=r_2$, the factored form is $y=a(x-r_1)(x-r_2)$.
Given intercepts $(-4,0)$ and $(2,0)$, substitute $r_1=-4$, $r_2=2$:
$y=a(x+4)(x-2)$

Step2: Substitute point (0,-4) to find $a$

Plug $x=0$, $y=-4$ into the equation:
$-4=a(0+4)(0-2)$
Simplify the right-hand side:
$-4=a(4)(-2) \implies -4=-8a$
Solve for $a$:
$a=\frac{-4}{-8}=\frac{1}{2}$

Step3: Write final factored equation

Substitute $a=\frac{1}{2}$ back into the factored form:
$y=\frac{1}{2}(x+4)(x-2)$

Answer:

$\boldsymbol{y=\frac{1}{2}(x+4)(x-2)}$ (matches the second option)