Find the Quadratic Equation (-3,-2)

$(- 3, - 2)$

Step 1

$x = - 3$ and $x = - 2$ are the two real distinct solutions for the quadratic equation, which means that $x + 3$ and $x + 2$ are the factors of the quadratic equation.

$(x + 3) (x + 2) = 0$

Step 2

Expand $(x + 3) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$x (x + 2) + 3 (x + 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 2 + 3 (x + 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 2 + 3 x + 3 \cdot 2 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $3$ by $2$ .

$x^{2} + 2 x + 3 x + 6 = 0$

Add $2 x$ and $3 x$ .

$x^{2} + 5 x + 6 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 3, - 2}$ is $y = x^{2} + 5 x + 6$ .

$y = x^{2} + 5 x + 6$

Step 5

Find the Quadratic Equation (-3,-2)

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