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 $2$ .

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

Subtract $3 x$ from $2 x$ .

$y = x^{2} - x - 6$

Step 6