Find the Quadratic Equation -6 , 2

$- 6$ , $2$

Step 1

$x = - 6$ and $x = 2$ are the two real distinct solutions for the quadratic equation, which means that $x + 6$ and $x - 2$ are the factors of the quadratic equation.

$(x + 6) (x - 2) = 0$

Step 2

Expand $(x + 6) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$x (x - 2) + 6 (x - 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 6 (x - 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 6 x + 6 \cdot - 2 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $6$ by $- 2$ .

$x^{2} - 2 x + 6 x - 12 = 0$

Add $- 2 x$ and $6 x$ .

$x^{2} + 4 x - 12 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 6, 2}$ is $y = x^{2} + 4 x - 12$ .

$y = x^{2} + 4 x - 12$

Step 5

Find the Quadratic Equation -6 , 2

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