Find the Equation Given the Roots 4 , -3

$4$ , $- 3$

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

$y = 0$ at the roots

The root at $x = 4$ was found by solving for $x$ when $x - (4) = y$ and $y = 0$ .

The factor is $x - 4$

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

The factor is $x + 3$

Combine all the factors into a single equation.

$y = (x - 4) (x + 3)$

Multiply all the factors to simplify the equation $y = (x - 4) (x + 3)$ .

Expand $(x - 4) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$y = x (x + 3) - 4 (x + 3)$

Apply the distributive property.

$y = x \cdot x + x \cdot 3 - 4 (x + 3)$

Apply the distributive property.

$y = x \cdot x + x \cdot 3 - 4 x - 4 \cdot 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 3 - 4 x - 4 \cdot 3$

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

$y = x^{2} + 3 \cdot x - 4 x - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$y = x^{2} + 3 x - 4 x - 12$

Subtract $4 x$ from $3 x$ .

$y = x^{2} - x - 12$