Find the Equation Given the Roots 0 , 7

$0$ , $7$

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

The factor is $x$

Step 3

The root at $x = 7$ was found by solving for $x$ when $x - (7) = y$ and $y = 0$ .

The factor is $x - 7$

Step 4

Combine all the factors into a single equation.

$y = (x) (x - 7)$

Step 5

Multiply all the factors to simplify the equation $y = (x) (x - 7)$ .

Apply the distributive property.

$y = x \cdot x + x \cdot - 7$

Simplify the expression.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 7$

Move $- 7$ to the left of $x$ .

$y = x^{2} - 7 x$

Step 6