Find the Quadratic Equation (-3,12)

$(- 3, 12)$

Step 1

$x = - 3$ and $x = 12$ are the two real distinct solutions for the quadratic equation, which means that $x + 3$ and $x - 12$ are the factors of the quadratic equation.

$(x + 3) (x - 12) = 0$

Step 2

Expand $(x + 3) (x - 12)$ using the FOIL Method.

Apply the distributive property.

$x (x - 12) + 3 (x - 12) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 12 + 3 (x - 12) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 12 + 3 x + 3 \cdot - 12 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 12 + 3 x + 3 \cdot - 12 = 0$

Move $- 12$ to the left of $x$ .

$x^{2} - 12 \cdot x + 3 x + 3 \cdot - 12 = 0$

Multiply $3$ by $- 12$ .

$x^{2} - 12 x + 3 x - 36 = 0$

Add $- 12 x$ and $3 x$ .

$x^{2} - 9 x - 36 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 3, 12}$ is $y = x^{2} - 9 x - 36$ .

$y = x^{2} - 9 x - 36$

Step 5

Find the Quadratic Equation (-3,12)

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