A quadratic relation has zeros at -2 and 7 and passes through the point (-1, -16). Determine the equation of this parabola in factored form.

Answer 1

If a quadratic relation has zeros at -2 and 7, then the factors of the quadratic equation are $(x+2)$ and $(x-7)$.

Thus, the quadratic equation in factored form is $y=a(x+2)(x-7)$, where $a$ is a constant.

To solve for $a$, we substitute the coordinates of the given point $(-1, -16)$ into the equation.

$-16=a((-1)+2)((-1)-7)$
$-16=a(1)(-8)$
$-16=-8a$
$a=2$

Therefore, the equation of the quadratic relation in factored form is $y=2(x+2)(x-7)$.