Precalculus Examples

$- 3$ , $3$

Step 1

Roots are the points where the graph intercepts with the x-axis $(y = 0)$ .

$y = 0$ at the roots

Step 2

The root at $x = - 3$ was found by solving for $x$ when $x - (- 3) = y$ and $y = 0$ .

The factor is $x + 3$

Step 3

The root at $x = 3$ was found by solving for $x$ when $x - (3) = y$ and $y = 0$ .

The factor is $x - 3$

Step 4

Combine all the factors into a single equation.

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

Step 5

Multiply all the factors to simplify the equation $y = (x + 3) (x - 3)$ .

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Step 5.1

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

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Step 5.1.1

Apply the distributive property.

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

Step 5.1.2

Apply the distributive property.

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

Step 5.1.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$

Step 5.2

Simplify terms.

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Step 5.2.1

Combine the opposite terms in $x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$ .

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Step 5.2.1.1

Reorder the factors in the terms $x \cdot - 3$ and $3 x$ .

$y = x \cdot x - 3 x + 3 x + 3 \cdot - 3$

Step 5.2.1.2

Add $- 3 x$ and $3 x$ .

$y = x \cdot x + 0 + 3 \cdot - 3$

Step 5.2.1.3

Add $x \cdot x$ and $0$ .

$y = x \cdot x + 3 \cdot - 3$

Step 5.2.2

Simplify each term.

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Step 5.2.2.1

Multiply $x$ by $x$ .

$y = x^{2} + 3 \cdot - 3$

Step 5.2.2.2

Multiply $3$ by $- 3$ .

$y = x^{2} - 9$

Step 6

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