Question

select the correct answer
the graph of quadratic function $f$ has $x$-intercepts of $(-7,0)$ and $(-4,0)$. which equation could represent function $f$?
a. $f(x)=2(x + 7)(x - 4)$
b. $f(x)=-3(x + 7)(x + 4)$
c. $f(x)=-\frac{1}{2}(x - 7)(x + 4)$
d. $f(x)=(x - 7)(x - 4)$

Explanation:

Step1: Recall intercept form of quadratic

If a quadratic has x-intercepts at $(r_1,0)$ and $(r_2,0)$, its form is $f(x)=a(x-r_1)(x-r_2)$ where $a
eq0$.

Step2: Substitute given intercepts

Intercepts are $(-7,0)$ and $(-4,0)$, so $r_1=-7$, $r_2=-4$.
$f(x)=a(x-(-7))(x-(-4))=a(x+7)(x+4)$

Step3: Match to options

Only option B follows this form with $a=-3$.

Answer:

B. $f(x) = -3(x + 7) (x + 4)$