Precalculus Examples

$- 3$ , $3$

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

$y = 0$ at the roots

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

The factor is $x + 3$

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

The factor is $x - 3$

Combine all the factors into a single equation.

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

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

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

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

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

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

Multiply $3$ by $- 3$ .

$y = x^{2} - 3 x + 3 x - 9$

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

$y = x^{2} + 0 - 9$

Add $x^{2}$ and $0$ .

$y = x^{2} - 9$

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