Find the Quadratic Equation (3,-3)

$(3, - 3)$

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify terms.

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

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

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

Subtract $3 x$ from $3 x$ .

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

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

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $3$ .

$x^{2} - 9 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${3, - 3}$ is $y = x^{2} - 9$ .

$y = x^{2} - 9$

Step 5

Find the Quadratic Equation (3,-3)

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