Find the Quadratic Equation (negative infinity,-6)

$(- \infty, - 6)$

Step 1

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

$(x + \infty) (x + 6) = 0$

Step 2

Expand $(x + \infty) (x + 6)$ using the FOIL Method.

Apply the distributive property.

$x (x + 6) + \infty (x + 6) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 6 + \infty (x + 6) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 6 + \infty x + \infty \cdot 6 = 0$

Step 3

Simplify each term.

Multiply $x$ by $x$ .

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

Move $6$ to the left of $x$ .

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

A non-zero constant times infinity is infinity.

$x^{2} + 6 x + \infty x + \infty = 0$

Step 4

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

$y = x^{2} + 6 x + \infty x + \infty$

Step 5

Find the Quadratic Equation (negative infinity,-6)

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