Find the x and y Intercepts f(x)=(5x^2-45x+100)/(-4x^2+20x)

$f (x) = \frac{5 x^{2} - 45 x + 100}{- 4 x^{2} + 20 x}$

Find the x-intercepts.

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

$0 = \frac{5 x^{2} - 45 x + 100}{- 4 x^{2} + 20 x}$

Solve the equation.

Set the numerator equal to zero.

$5 x^{2} - 45 x + 100 = 0$

Solve the equation for $x$ .

Factor the left side of the equation.

Factor $5$ out of $5 x^{2} - 45 x + 100$ .

Factor $5$ out of $5 x^{2}$ .

$5 (x^{2}) - 45 x + 100 = 0$

Factor $5$ out of $- 45 x$ .

$5 (x^{2}) + 5 (- 9 x) + 100 = 0$

Factor $5$ out of $100$ .

$5 x^{2} + 5 (- 9 x) + 5 \cdot 20 = 0$

Factor $5$ out of $5 x^{2} + 5 (- 9 x)$ .

$5 (x^{2} - 9 x) + 5 \cdot 20 = 0$

Factor $5$ out of $5 (x^{2} - 9 x) + 5 \cdot 20$ .

$5 (x^{2} - 9 x + 20) = 0$

Factor.

Factor $x^{2} - 9 x + 20$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $20$ and whose sum is $- 9$ .

$- 5, - 4$

Write the factored form using these integers.

$5 ((x - 5) (x - 4)) = 0$

Remove unnecessary parentheses.

$5 (x - 5) (x - 4) = 0$

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

$x - 5 = 0$

$x - 4 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $5 (x - 5) (x - 4) = 0$ true.

$x = 5, 4$

Exclude the solutions that do not make $0 = \frac{5 x^{2} - 45 x + 100}{- 4 x^{2} + 20 x}$ true.

$x = 4$

x-intercept(s) in point form.

x-intercept(s): $(4, 0)$

Find the y-intercepts.

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

$y = \frac{5 {(0)}^{2} - 45 \cdot 0 + 100}{- 4 {(0)}^{2} + 20 (0)}$

The equation has an undefined fraction.

Undefined

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

y-intercept(s): $None$

List the intersections.

x-intercept(s): $(4, 0)$

y-intercept(s): $None$

Find the x and y Intercepts f(x)=(5x^2-45x+100)/(-4x^2+20x)

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