Find the Equation Given the Roots -4 , 2

$- 4$ , $2$

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

The factor is $x + 4$

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.

$y = (x + 4) (x - 2)$

Step 5

Multiply all the factors to simplify the equation $y = (x + 4) (x - 2)$ .

Expand $(x + 4) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$y = x (x - 2) + 4 (x - 2)$

Apply the distributive property.

$y = x \cdot x + x \cdot - 2 + 4 (x - 2)$

Apply the distributive property.

$y = x \cdot x + x \cdot - 2 + 4 x + 4 \cdot - 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $4$ by $- 2$ .

$y = x^{2} - 2 x + 4 x - 8$

Add $- 2 x$ and $4 x$ .

$y = x^{2} + 2 x - 8$

Step 6