Evaluate y=a(x-h)^2+k

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

Step 1

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $h$ .

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

Multiply $h$ by $h$ .

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

Move $x$ .

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

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

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

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify the expression.

Move $a x^{2}$ .

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

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

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