Algebra Examples

$\frac{- x^{2} + 5 x}{2 x^{2}}$

Step 1

Write $\frac{- x^{2} + 5 x}{2 x^{2}}$ as an equation.

$y = \frac{- x^{2} + 5 x}{2 x^{2}}$

Step 2

Find the x-intercepts.

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Step 2.1

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

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

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

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

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

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

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Step 2.2.2.1.1

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

$- x \cdot x + 5 x = 0$

Step 2.2.2.1.2

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

$- x \cdot x - x \cdot - 5 = 0$

Step 2.2.2.1.3

Factor $- x$ out of $- x (x) - x (- 5)$ .

$- x (x - 5) = 0$

Step 2.2.2.2

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

$x = 0$

$x - 5 = 0$

Step 2.2.2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.2.2.4

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

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Step 2.2.2.4.1

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

$x - 5 = 0$

Step 2.2.2.4.2

Add $5$ to both sides of the equation.

$x = 5$

Step 2.2.2.5

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

$x = 0, 5$

Step 2.2.3

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

$x = 5$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(5, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

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

$y = \frac{- {(0)}^{2} + 5 (0)}{2 {(0)}^{2}}$

Step 3.2

The equation has an undefined fraction.

Undefined

Step 3.3

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

y-intercept(s): $None$

Step 4

List the intersections.

x-intercept(s): $(5, 0)$

y-intercept(s): $None$

Step 5