Question

What is the quadratic function that is created with roots -10 and -4 and a vertex at (-7, -9)?

Answer 1

Any quadratic function with roots -10 and -4 is of form
$f(x)=a(x+10)(x+4)$

Since the given vertex, $(-7,-9)$, is a point on the graph of $f(x)$ :
$-9=a(-7+10)(-7+4)\\-9=a(3)(-3)\\-9=-9a\\a=1$

Therefore the required quadratic function is $f(x)=1(x+10)(x+4)$, which is same as $\boxed{f(x)=x^2+14x+40}$