Find the Equation Given the Roots -3 , -2

$- 3$ , $- 2$

Step 1

Roots are the points where the graph intercepts with the x-axis $(y = 0)$ .

$y = 0$ at the roots

Step 2

The root at $x = - 3$ was found by solving for $x$ when $x - (- 3) = y$ and $y = 0$ .

The factor is $x + 3$

Step 3

The root at $x = - 2$ was found by solving for $x$ when $x - (- 2) = y$ and $y = 0$ .

The factor is $x + 2$

Step 4

Combine all the factors into a single equation.

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

Step 5

Multiply all the factors to simplify the equation $y = (x + 3) (x + 2)$ .

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $3$ by $2$ .

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

Add $2 x$ and $3 x$ .

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

Step 6