Find the Equation Given the Roots 8 , -5

$8$ , $- 5$

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

The factor is $x - 8$

Step 3

The root at $x = - 5$ was found by solving for $x$ when $x - (- 5) = y$ and $y = 0$ .

The factor is $x + 5$

Step 4

Combine all the factors into a single equation.

$y = (x - 8) (x + 5)$

Step 5

Multiply all the factors to simplify the equation $y = (x - 8) (x + 5)$ .

Expand $(x - 8) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$y = x (x + 5) - 8 (x + 5)$

Apply the distributive property.

$y = x \cdot x + x \cdot 5 - 8 (x + 5)$

Apply the distributive property.

$y = x \cdot x + x \cdot 5 - 8 x - 8 \cdot 5$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 5 - 8 x - 8 \cdot 5$

Move $5$ to the left of $x$ .

$y = x^{2} + 5 \cdot x - 8 x - 8 \cdot 5$

Multiply $- 8$ by $5$ .

$y = x^{2} + 5 x - 8 x - 40$

Subtract $8 x$ from $5 x$ .

$y = x^{2} - 3 x - 40$

Step 6