Find the Quadratic Equation (-4,-9)

$(- 4, - 9)$

Step 1

$x = - 4$ and $x = - 9$ are the two real distinct solutions for the quadratic equation, which means that $x + 4$ and $x + 9$ are the factors of the quadratic equation.

$(x + 4) (x + 9) = 0$

Step 2

Expand $(x + 4) (x + 9)$ using the FOIL Method.

Apply the distributive property.

$x (x + 9) + 4 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 + 4 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 + 4 x + 4 \cdot 9 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 9 + 4 x + 4 \cdot 9 = 0$

Move $9$ to the left of $x$ .

$x^{2} + 9 \cdot x + 4 x + 4 \cdot 9 = 0$

Multiply $4$ by $9$ .

$x^{2} + 9 x + 4 x + 36 = 0$

Add $9 x$ and $4 x$ .

$x^{2} + 13 x + 36 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 4, - 9}$ is $y = x^{2} + 13 x + 36$ .

$y = x^{2} + 13 x + 36$

Step 5

Find the Quadratic Equation (-4,-9)

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