Question

write a quadratic function $h$ whose zeros are $-6$ and $5$.
$h(x) = \square$

Explanation:

Step1: Use zero factor form

If $r_1$ and $r_2$ are zeros, $h(x)=(x-r_1)(x-r_2)$. Here $r_1=-6$, $r_2=5$, so:
$h(x)=(x-(-6))(x-5)=(x+6)(x-5)$

Step2: Expand the product

Use distributive property (FOIL):
$h(x)=x\cdot x + x\cdot(-5) + 6\cdot x + 6\cdot(-5)$

Step3: Simplify terms

Combine like terms:
$h(x)=x^2 -5x +6x -30 = x^2 +x -30$

Answer:

$h(x)=x^2 + x - 30$