Find the Equation Given the Roots 5 , -3

$5$ , $- 3$

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

The factor is $x - 5$

Step 3

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

The factor is $x + 3$

Step 4

Combine all the factors into a single equation.

$y = (x - 5) (x + 3)$

Step 5

Multiply all the factors to simplify the equation $y = (x - 5) (x + 3)$ .

Expand $(x - 5) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$y = x (x + 3) - 5 (x + 3)$

Apply the distributive property.

$y = x \cdot x + x \cdot 3 - 5 (x + 3)$

Apply the distributive property.

$y = x \cdot x + x \cdot 3 - 5 x - 5 \cdot 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 3 - 5 x - 5 \cdot 3$

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

$y = x^{2} + 3 \cdot x - 5 x - 5 \cdot 3$

Multiply $- 5$ by $3$ .

$y = x^{2} + 3 x - 5 x - 15$

Subtract $5 x$ from $3 x$ .

$y = x^{2} - 2 x - 15$

Step 6