Find the Equation Given the Roots 0 , 2 , 4

$0$ , $2$ , $4$

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 $x = 2$ was found by solving for $x$ when $x - (2) = y$ and $y = 0$ .

The factor is $x - 2$

Step 4

The root at $x = 4$ was found by solving for $x$ when $x - (4) = y$ and $y = 0$ .

The factor is $x - 4$

Step 5

Combine all the factors into a single equation.

$y = (x) (x - 2) (x - 4)$

Step 6

Multiply all the factors to simplify the equation $y = (x) (x - 2) (x - 4)$ .

Simplify by multiplying through.

Apply the distributive property.

$y = (x \cdot x + x \cdot - 2) (x - 4)$

Simplify the expression.

Multiply $x$ by $x$ .

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

Move $- 2$ to the left of $x$ .

$y = (x^{2} - 2 \cdot x) (x - 4)$

Expand $(x^{2} - 2 x) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$y = x^{2} (x - 4) - 2 x (x - 4)$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $1$ .

$y = x^{3} + x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4$

Move $- 4$ to the left of $x^{2}$ .

$y = x^{3} - 4 \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 4$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$y = x^{3} - 4 x^{2} - 2 (x \cdot x) - 2 x \cdot - 4$

Multiply $x$ by $x$ .

$y = x^{3} - 4 x^{2} - 2 x^{2} - 2 x \cdot - 4$

Multiply $- 4$ by $- 2$ .

$y = x^{3} - 4 x^{2} - 2 x^{2} + 8 x$

Subtract $2 x^{2}$ from $- 4 x^{2}$ .

$y = x^{3} - 6 x^{2} + 8 x$

Step 7

Find the Equation Given the Roots 0 , 2 , 4

Related Questions

Support LCMGCF.com by disabling your adblocker.