Precalculus Examples

$y - 2 = - 4 {(x - 7)}^{2}$

Step 1

Solve for $y$ .

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Step 1.1

Simplify $- 4 {(x - 7)}^{2}$ .

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Step 1.1.1

Rewrite.

$y - 2 = 0 + 0 - 4 {(x - 7)}^{2}$

Step 1.1.2

Rewrite ${(x - 7)}^{2}$ as $(x - 7) (x - 7)$ .

$y - 2 = - 4 ((x - 7) (x - 7))$

Step 1.1.3

Expand $(x - 7) (x - 7)$ using the FOIL Method.

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Step 1.1.3.1

Apply the distributive property.

$y - 2 = - 4 (x (x - 7) - 7 (x - 7))$

Step 1.1.3.2

Apply the distributive property.

$y - 2 = - 4 (x \cdot x + x \cdot - 7 - 7 (x - 7))$

Step 1.1.3.3

Apply the distributive property.

$y - 2 = - 4 (x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7)$

Step 1.1.4

Simplify and combine like terms.

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Step 1.1.4.1

Simplify each term.

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Step 1.1.4.1.1

Multiply $x$ by $x$ .

$y - 2 = - 4 (x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7)$

Step 1.1.4.1.2

Move $- 7$ to the left of $x$ .

$y - 2 = - 4 (x^{2} - 7 \cdot x - 7 x - 7 \cdot - 7)$

Step 1.1.4.1.3

Multiply $- 7$ by $- 7$ .

$y - 2 = - 4 (x^{2} - 7 x - 7 x + 49)$

Step 1.1.4.2

Subtract $7 x$ from $- 7 x$ .

$y - 2 = - 4 (x^{2} - 14 x + 49)$

Step 1.1.5

Apply the distributive property.

$y - 2 = - 4 x^{2} - 4 (- 14 x) - 4 \cdot 49$

Step 1.1.6

Simplify.

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Step 1.1.6.1

Multiply $- 14$ by $- 4$ .

$y - 2 = - 4 x^{2} + 56 x - 4 \cdot 49$

Step 1.1.6.2

Multiply $- 4$ by $49$ .

$y - 2 = - 4 x^{2} + 56 x - 196$

Step 1.2

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

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Step 1.2.1

Add $2$ to both sides of the equation.

$y = - 4 x^{2} + 56 x - 196 + 2$

Step 1.2.2

Add $- 196$ and $2$ .

$y = - 4 x^{2} + 56 x - 194$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 3

The standard form is $- 4 x^{2} + 56 x - 194$ .

$y = - 4 x^{2} + 56 x - 194$

Step 4