Question

Which equation, when graphed, has x-intercepts at (-1,0) and (-5,0) and a y-intercept at (0, -30)?

Answer 1

If a function has roots -1 and -5, it must be in the form

$f(x)=a(x+1)(x+5)$

We can fix the coefficient a by imposing the passing through (0,-30):

$f(0)=-30=a(1)(5)\iff a=-6$

So, the function is

$f(x)=-6(x+1)(x+5)$