Algebra Examples

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

Step 1

Rewrite the function as an equation.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

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

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Step 2.1.2.1

Apply the distributive property.

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

Step 2.1.2.2

Apply the distributive property.

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

Step 2.1.2.3

Apply the distributive property.

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

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

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

Step 2.1.3.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3.1.3

Rewrite using the commutative property of multiplication.

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

Step 2.1.3.1.4

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

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Step 2.1.3.1.4.1

Move $h$ .

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

Step 2.1.3.1.4.2

Multiply $h$ by $h$ .

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

Step 2.1.3.1.5

Multiply $- 1$ by $- 1$ .

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

Step 2.1.3.1.6

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

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

Step 2.1.3.2

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

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Step 2.1.3.2.1

Move $x$ .

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

Step 2.1.3.2.2

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

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

Step 2.1.4

Apply the distributive property.

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

Step 2.1.5

Rewrite using the commutative property of multiplication.

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

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $a x^{2}$ .

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

Step 2.2.2

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

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