Write as an Equation f(x)=a(x-h)^2

$f (x) = a {(x - h)}^{2}$

Rewrite the function as an equation.

$y = a {(x - h)}^{2}$

Simplify $a {(x - h)}^{2}$ .

Rewrite ${(x - h)}^{2}$ as $(x - h) (x - h)$ .

$y = a ((x - h) (x - h))$

Expand $(x - h) (x - h)$ using the FOIL Method.

Apply the distributive property.

$y = a (x (x - h) - h (x - h))$

Apply the distributive property.

$y = a (x \cdot x + x (- h) - h (x - h))$

Apply the distributive property.

$y = a (x \cdot x + x (- h) - h x - h (- h))$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = a (x^{2} + x (- h) - h x - h (- h))$

Rewrite using the commutative property of multiplication.

$y = a (x^{2} - x h - h x - h (- h))$

Rewrite using the commutative property of multiplication.

$y = a (x^{2} - x h - h x - 1 \cdot - 1 h \cdot h)$

Multiply $h$ by $h$ by adding the exponents.

Move $h$ .

$y = a (x^{2} - x h - h x - 1 \cdot - 1 (h \cdot h))$

Multiply $h$ by $h$ .

$y = a (x^{2} - x h - h x - 1 \cdot - 1 h^{2})$

Multiply $- 1$ by $- 1$ .

$y = a (x^{2} - x h - h x + 1 h^{2})$

Multiply $h^{2}$ by $1$ .

$y = a (x^{2} - x h - h x + h^{2})$

Subtract $h x$ from $- x h$ .

Move $x$ .

$y = a (x^{2} - h x - h x + h^{2})$

Subtract $h x$ from $- h x$ .

$y = a (x^{2} - 2 h x + h^{2})$

Apply the distributive property.

$y = a x^{2} + a (- 2 h x) + a h^{2}$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$y = a x^{2} - 2 a h x + a h^{2}$

Move $a x^{2}$ .

$y = - 2 a h x + a h^{2} + a x^{2}$

Reorder $- 2 a h x$ and $a h^{2}$ .

$y = a h^{2} - 2 a h x + a x^{2}$