Answer
See below
Work Step by Step
The intercept form of the quadratic function is:
$y=a(x-p)(x-q)$
Since the x-intercepts are $-2$ and $4$, we have:
$y=a(x-(-2)(x-4)\\
y=(x+2)(x-4)$
We know that $(1,3)$ is on the graph. After substituting $x=1$ into the equation, we get $y=3$.
Hence, $3=a(1+2)(1-4)\\
\rightarrow a=-\frac{1}{3}$
The function is:
$y=-\frac{1}{3}(x+2)(x-4)$
