Find the Equation Given the Roots -4 , -1

$- 4$ , $- 1$

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 $x = - 1$ was found by solving for $x$ when $x - (- 1) = y$ and $y = 0$ .

The factor is $x + 1$

Step 4

Combine all the factors into a single equation.

$y = (x + 4) (x + 1)$

Step 5

Multiply all the factors to simplify the equation $y = (x + 4) (x + 1)$ .

Expand $(x + 4) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$y = x (x + 1) + 4 (x + 1)$

Apply the distributive property.

$y = x \cdot x + x \cdot 1 + 4 (x + 1)$

Apply the distributive property.

$y = x \cdot x + x \cdot 1 + 4 x + 4 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 1 + 4 x + 4 \cdot 1$

Multiply $x$ by $1$ .

$y = x^{2} + x + 4 x + 4 \cdot 1$

Multiply $4$ by $1$ .

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

Add $x$ and $4 x$ .

$y = x^{2} + 5 x + 4$

Step 6