Precalculus Examples

$(6, - 3)$

$x = 6$ and $x = - 3$ are the two real distinct solutions for the quadratic equation, which means that $x - 6$ and $x + 3$ are the factors of the quadratic equation.

$(x - 6) (x + 3) = 0$

Expand $(x - 6) (x + 3)$ using the FOIL Method.

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Apply the distributive property.

$x (x + 3) - 6 (x + 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 6 (x + 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 6 x - 6 \cdot 3 = 0$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 - 6 x - 6 \cdot 3 = 0$

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

$x^{2} + 3 \cdot x - 6 x - 6 \cdot 3 = 0$

Multiply $- 6$ by $3$ .

$x^{2} + 3 x - 6 x - 18 = 0$

Subtract $6 x$ from $3 x$ .

$x^{2} - 3 x - 18 = 0$

The standard quadratic equation using the given set of solutions ${6, - 3}$ is $y = x^{2} - 3 x - 18$ .

$y = x^{2} - 3 x - 18$

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