Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Simplify the right side.

Tap for more steps...

Step 1.1.1

Simplify each term.

Tap for more steps...

Step 1.1.1.1

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

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

Step 1.1.1.2

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

Tap for more steps...

Step 1.1.1.2.1

Apply the distributive property.

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

Step 1.1.1.2.2

Apply the distributive property.

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

Step 1.1.1.2.3

Apply the distributive property.

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

Step 1.1.1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.1.1.3.1

Simplify each term.

Tap for more steps...

Step 1.1.1.3.1.1

Multiply $x$ by $x$ .

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

Step 1.1.1.3.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.1.1.3.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.1.1.3.1.4

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

Tap for more steps...

Step 1.1.1.3.1.4.1

Move $h$ .

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

Step 1.1.1.3.1.4.2

Multiply $h$ by $h$ .

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

Step 1.1.1.3.1.5

Multiply $- 1$ by $- 1$ .

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

Step 1.1.1.3.1.6

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

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

Step 1.1.1.3.2

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

Tap for more steps...

Step 1.1.1.3.2.1

Move $x$ .

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

Step 1.1.1.3.2.2

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

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

Step 1.1.1.4

Apply the distributive property.

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

Step 1.1.1.5

Rewrite using the commutative property of multiplication.

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

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

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

Step 1.2.4

Subtract $k$ from both sides of the equation.

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Add $k$ to both sides of the equation.

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