Find the Quadratic Equation (3,-11)

$(3, - 11)$

Step 1

$x = 3$ and $x = - 11$ are the two real distinct solutions for the quadratic equation, which means that $x - 3$ and $x + 11$ are the factors of the quadratic equation.

$(x - 3) (x + 11) = 0$

Step 2

Expand $(x - 3) (x + 11)$ using the FOIL Method.

Apply the distributive property.

$x (x + 11) - 3 (x + 11) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 11 - 3 (x + 11) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 11 - 3 x - 3 \cdot 11 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 11 - 3 x - 3 \cdot 11 = 0$

Move $11$ to the left of $x$ .

$x^{2} + 11 \cdot x - 3 x - 3 \cdot 11 = 0$

Multiply $- 3$ by $11$ .

$x^{2} + 11 x - 3 x - 33 = 0$

Subtract $3 x$ from $11 x$ .

$x^{2} + 8 x - 33 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${3, - 11}$ is $y = x^{2} + 8 x - 33$ .

$y = x^{2} + 8 x - 33$

Step 5

Find the Quadratic Equation (3,-11)

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