Find the Quadratic Equation (-9,-7)

$(- 9, - 7)$

Step 1

$x = - 9$ and $x = - 7$ are the two real distinct solutions for the quadratic equation, which means that $x + 9$ and $x + 7$ are the factors of the quadratic equation.

$(x + 9) (x + 7) = 0$

Step 2

Expand $(x + 9) (x + 7)$ using the FOIL Method.

Apply the distributive property.

$x (x + 7) + 9 (x + 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 7 + 9 (x + 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 7 + 9 x + 9 \cdot 7 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 7 + 9 x + 9 \cdot 7 = 0$

Move $7$ to the left of $x$ .

$x^{2} + 7 \cdot x + 9 x + 9 \cdot 7 = 0$

Multiply $9$ by $7$ .

$x^{2} + 7 x + 9 x + 63 = 0$

Add $7 x$ and $9 x$ .

$x^{2} + 16 x + 63 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 9, - 7}$ is $y = x^{2} + 16 x + 63$ .

$y = x^{2} + 16 x + 63$

Step 5

Find the Quadratic Equation (-9,-7)

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