Finite Math Examples

$(y - 16) = - 36 {(x - (- 3))}^{2}$

Step 1

Simplify $- 36 {(x - (- 3))}^{2}$ .

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Step 1.1

Rewrite.

$y - 16 = 0 + 0 - 36 {(x - (- 3))}^{2}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $- 1$ by $- 3$ .

$y - 16 = - 36 {(x + 3)}^{2}$

Step 1.2.2

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$y - 16 = - 36 ((x + 3) (x + 3))$

Step 1.3

Expand $(x + 3) (x + 3)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$y - 16 = - 36 (x (x + 3) + 3 (x + 3))$

Step 1.3.2

Apply the distributive property.

$y - 16 = - 36 (x \cdot x + x \cdot 3 + 3 (x + 3))$

Step 1.3.3

Apply the distributive property.

$y - 16 = - 36 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3)$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$y - 16 = - 36 (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3)$

Step 1.4.1.2

Move $3$ to the left of $x$ .

$y - 16 = - 36 (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3)$

Step 1.4.1.3

Multiply $3$ by $3$ .

$y - 16 = - 36 (x^{2} + 3 x + 3 x + 9)$

Step 1.4.2

Add $3 x$ and $3 x$ .

$y - 16 = - 36 (x^{2} + 6 x + 9)$

Step 1.5

Apply the distributive property.

$y - 16 = - 36 x^{2} - 36 (6 x) - 36 \cdot 9$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $6$ by $- 36$ .

$y - 16 = - 36 x^{2} - 216 x - 36 \cdot 9$

Step 1.6.2

Multiply $- 36$ by $9$ .

$y - 16 = - 36 x^{2} - 216 x - 324$

Step 2

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

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Step 2.1

Add $16$ to both sides of the equation.

$y = - 36 x^{2} - 216 x - 324 + 16$

Step 2.2

Add $- 324$ and $16$ .

$y = - 36 x^{2} - 216 x - 308$