Find the Quadratic Equation (-9,2)

$(- 9, 2)$

Step 1

$x = - 9$ and $x = 2$ are the two real distinct solutions for the quadratic equation, which means that $x + 9$ and $x - 2$ are the factors of the quadratic equation.

$(x + 9) (x - 2) = 0$

Step 2

Expand $(x + 9) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$x (x - 2) + 9 (x - 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 9 (x - 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 9 x + 9 \cdot - 2 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 + 9 x + 9 \cdot - 2 = 0$

Move $- 2$ to the left of $x$ .

$x^{2} - 2 \cdot x + 9 x + 9 \cdot - 2 = 0$

Multiply $9$ by $- 2$ .

$x^{2} - 2 x + 9 x - 18 = 0$

Add $- 2 x$ and $9 x$ .

$x^{2} + 7 x - 18 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 9, 2}$ is $y = x^{2} + 7 x - 18$ .

$y = x^{2} + 7 x - 18$

Step 5

Find the Quadratic Equation (-9,2)

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