Find the Quadratic Equation (6,-9)

$(6, - 9)$

Step 1

$x = 6$ and $x = - 9$ are the two real distinct solutions for the quadratic equation, which means that $x - 6$ and $x + 9$ are the factors of the quadratic equation.

$(x - 6) (x + 9) = 0$

Step 2

Expand $(x - 6) (x + 9)$ using the FOIL Method.

Apply the distributive property.

$x (x + 9) - 6 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 - 6 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 - 6 x - 6 \cdot 9 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 9 - 6 x - 6 \cdot 9 = 0$

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

$x^{2} + 9 \cdot x - 6 x - 6 \cdot 9 = 0$

Multiply $- 6$ by $9$ .

$x^{2} + 9 x - 6 x - 54 = 0$

Subtract $6 x$ from $9 x$ .

$x^{2} + 3 x - 54 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${6, - 9}$ is $y = x^{2} + 3 x - 54$ .

$y = x^{2} + 3 x - 54$

Step 5

Find the Quadratic Equation (6,-9)

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