Find the x and y Intercepts f(x)=(2x^2-7x+6)/(x^2-8x)

$f (x) = \frac{2 x^{2} - 7 x + 6}{x^{2} - 8 x}$

Step 1

Find the x-intercepts.

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

$0 = \frac{2 x^{2} - 7 x + 6}{x^{2} - 8 x}$

Solve the equation.

Set the numerator equal to zero.

$2 x^{2} - 7 x + 6 = 0$

Solve the equation for $x$ .

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 6 = 12$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$2 x^{2} - 7 x + 6 = 0$

Rewrite $- 7$ as $- 3$ plus $- 4$

$2 x^{2} + (- 3 - 4) x + 6 = 0$

Apply the distributive property.

$2 x^{2} - 3 x - 4 x + 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x) - 4 x + 6 = 0$

Factor out the greatest common factor (GCF) from each group.

$x (2 x - 3) - 2 (2 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (x - 2) = 0$

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

$2 x - 3 = 0$

$x - 2 = 0$

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $(2 x - 3) (x - 2) = 0$ true.

$x = \frac{3}{2}, 2$

x-intercept(s) in point form.

x-intercept(s): $(\frac{3}{2}, 0), (2, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{2 {(0)}^{2} - 7 \cdot 0 + 6}{{(0)}^{2} - 8 \cdot 0}$

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): $None$

Step 3

List the intersections.

x-intercept(s): $(\frac{3}{2}, 0), (2, 0)$

y-intercept(s): $None$

Step 4

Find the x and y Intercepts f(x)=(2x^2-7x+6)/(x^2-8x)

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