Question

nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. which equation represents the average of the x-intercepts for $f(x) = 4x^2 - 24x + 20$?
$\frac{-5-1}{2}=-3$
$\frac{-10-2}{2}=-4$
$\frac{1+5}{2}=3$
$\frac{2+10}{2}=4$

Explanation:

Step1: Factor the quadratic

First, factor out 4: $f(x)=4(x^2-6x+5)$. Then factor the trinomial: $f(x)=4(x-1)(x-5)$

Step2: Find x-intercepts

Set $f(x)=0$, so $x-1=0$ or $x-5=0$. Thus, $x=1$ and $x=5$.

Step3: Calculate average of intercepts

Average = $\frac{\text{Sum of intercepts}}{2}$
$\frac{1+5}{2}=3$

Answer:

$\frac{1+5}{2}=3$