Question

Write the equation of the following graph in intercept form.

Answer 1

Answer:

A) $f(x)=0.2(x+2)(x-5)$

Step-by-step explanation:

The graph has x-intercepts at $x=5$ and $x=-2$, so our factors for the polynomial will be $x+2$ and $x-5$. This means we can rule out options B and D.

Our graph also has a y-intercept of $y=-2$ when $x=0$, so if we let $f(x)=-2$ and $x=0$, we can find the multiplier:

$f(x)=a(x+2)(x-5)\\-2=a(0+2)(0-5)\\-2=a(2)(-5)\\-2=-10a\\\frac{1}{5}=a\\0.2=a$

Thus, the correct equation is A) $f(x)=0.2(x+2)(x-5)$