Find the Equation Given the Roots 4 , -8

$4$ , $- 8$

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 $x = - 8$ was found by solving for $x$ when $x - (- 8) = y$ and $y = 0$ .

The factor is $x + 8$

Step 4

Combine all the factors into a single equation.

$y = (x - 4) (x + 8)$

Step 5

Multiply all the factors to simplify the equation $y = (x - 4) (x + 8)$ .

Expand $(x - 4) (x + 8)$ using the FOIL Method.

Apply the distributive property.

$y = x (x + 8) - 4 (x + 8)$

Apply the distributive property.

$y = x \cdot x + x \cdot 8 - 4 (x + 8)$

Apply the distributive property.

$y = x \cdot x + x \cdot 8 - 4 x - 4 \cdot 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $8$ to the left of $x$ .

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

Multiply $- 4$ by $8$ .

$y = x^{2} + 8 x - 4 x - 32$

Subtract $4 x$ from $8 x$ .

$y = x^{2} + 4 x - 32$

Step 6