Find the Quadratic Equation (-1,-3)

$(- 1, - 3)$

Step 1

$x = - 1$ and $x = - 3$ are the two real distinct solutions for the quadratic equation, which means that $x + 1$ and $x + 3$ are the factors of the quadratic equation.

$(x + 1) (x + 3) = 0$

Step 2

Expand $(x + 1) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$x (x + 3) + 1 (x + 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 3 + 1 (x + 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 3 + 1 x + 1 \cdot 3 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 + 1 x + 1 \cdot 3 = 0$

Move $3$ to the left of $x$ .

$x^{2} + 3 \cdot x + 1 x + 1 \cdot 3 = 0$

Multiply $x$ by $1$ .

$x^{2} + 3 x + x + 1 \cdot 3 = 0$

Multiply $3$ by $1$ .

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

Add $3 x$ and $x$ .

$x^{2} + 4 x + 3 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 1, - 3}$ is $y = x^{2} + 4 x + 3$ .

$y = x^{2} + 4 x + 3$

Step 5

Find the Quadratic Equation (-1,-3)

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