Find the x and y Intercepts f(x)=(-4x^2+4x)/(5x^2-25x+20)

$f (x) = \frac{- 4 x^{2} + 4 x}{5 x^{2} - 25 x + 20}$

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{- 4 x^{2} + 4 x}{5 x^{2} - 25 x + 20}$

Solve the equation.

Set the numerator equal to zero.

$- 4 x^{2} + 4 x = 0$

Solve the equation for $x$ .

Factor $- 4 x$ out of $- 4 x^{2} + 4 x$ .

Factor $- 4 x$ out of $- 4 x^{2}$ .

$- 4 x \cdot x + 4 x = 0$

Factor $- 4 x$ out of $4 x$ .

$- 4 x \cdot x - 4 x \cdot - 1 = 0$

Factor $- 4 x$ out of $- 4 x (x) - 4 x (- 1)$ .

$- 4 x (x - 1) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $- 4 x (x - 1) = 0$ true.

$x = 0, 1$

Exclude the solutions that do not make $0 = \frac{- 4 x^{2} + 4 x}{5 x^{2} - 25 x + 20}$ true.

$x = 0$

x-intercept(s) in point form.

x-intercept(s): $(0, 0)$

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{- 4 {(0)}^{2} + 4 (0)}{5 {(0)}^{2} - 25 \cdot 0 + 20}$

Solve the equation.

Remove parentheses.

$y = \frac{- 4 \cdot 0^{2} + 4 (0)}{5 {(0)}^{2} - 25 \cdot 0 + 20}$

Remove parentheses.

$y = \frac{- 4 \cdot 0^{2} + 4 (0)}{5 \cdot 0^{2} - 25 \cdot 0 + 20}$

Remove parentheses.

$y = \frac{- 4 {(0)}^{2} + 4 (0)}{5 {(0)}^{2} - 25 \cdot 0 + 20}$

Simplify $\frac{- 4 {(0)}^{2} + 4 (0)}{5 {(0)}^{2} - 25 \cdot 0 + 20}$ .

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{- 4 \cdot 0 + 4 (0)}{5 \cdot 0^{2} - 25 \cdot 0 + 20}$

Multiply $- 4$ by $0$ .

$y = \frac{0 + 4 (0)}{5 \cdot 0^{2} - 25 \cdot 0 + 20}$

Multiply $4$ by $0$ .

$y = \frac{0 + 0}{5 \cdot 0^{2} - 25 \cdot 0 + 20}$

Add $0$ and $0$ .

$y = \frac{0}{5 \cdot 0^{2} - 25 \cdot 0 + 20}$

Simplify the denominator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{0}{5 \cdot 0 - 25 \cdot 0 + 20}$

Multiply $5$ by $0$ .

$y = \frac{0}{0 - 25 \cdot 0 + 20}$

Multiply $- 25$ by $0$ .

$y = \frac{0}{0 + 0 + 20}$

Add $0$ and $0$ .

$y = \frac{0}{0 + 20}$

Add $0$ and $20$ .

$y = \frac{0}{20}$

Divide $0$ by $20$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

List the intersections.

x-intercept(s): $(0, 0)$

y-intercept(s): $(0, 0)$

Find the x and y Intercepts f(x)=(-4x^2+4x)/(5x^2-25x+20)

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