Solve Using the Quadratic Formula y=a(x-h)^2+k

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

Move all terms to the left side of the equation and simplify.

Simplify the right side.

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.

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

Move all the expressions to the left side of the equation.

Subtract $a x^{2}$ from both sides of the equation.

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

Add $2 a h x$ to both sides of the equation.

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

Subtract $a h^{2}$ from both sides of the equation.

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

Subtract $k$ from both sides of the equation.

$y - a x^{2} + 2 a h x - a h^{2} - k = 0$

Move all terms not containing $y$ to the right side of the equation.

Add $a x^{2}$ to both sides of the equation.

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

Subtract $2 a h x$ from both sides of the equation.

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

Add $a h^{2}$ to both sides of the equation.

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

Add $k$ to both sides of the equation.

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

Solve Using the Quadratic Formula y=a(x-h)^2+k

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