Finite Math Examples

$f (x) = 2 x^{2} - 5 x$

Step 1

Find the x-intercepts.

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Step 1.1

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

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

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $2 x^{2} - 5 x = 0$ .

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

Step 1.2.2

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

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Step 1.2.2.1

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

$x (2 x) - 5 x = 0$

Step 1.2.2.2

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

$x (2 x) + x \cdot - 5 = 0$

Step 1.2.2.3

Factor $x$ out of $x (2 x) + x \cdot - 5$ .

$x (2 x - 5) = 0$

Step 1.2.3

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

$x = 0$

$2 x - 5 = 0$

Step 1.2.4

Set $x$ equal to $0$ .

$x = 0$

Step 1.2.5

Set $2 x - 5$ equal to $0$ and solve for $x$ .

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Step 1.2.5.1

Set $2 x - 5$ equal to $0$ .

$2 x - 5 = 0$

Step 1.2.5.2

Solve $2 x - 5 = 0$ for $x$ .

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Step 1.2.5.2.1

Add $5$ to both sides of the equation.

$2 x = 5$

Step 1.2.5.2.2

Divide each term in $2 x = 5$ by $2$ and simplify.

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Step 1.2.5.2.2.1

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Step 1.2.5.2.2.2

Simplify the left side.

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Step 1.2.5.2.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.5.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Step 1.2.5.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{2}$

Step 1.2.6

The final solution is all the values that make $x (2 x - 5) = 0$ true.

$x = 0, \frac{5}{2}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (\frac{5}{2}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 2 \cdot 0^{2} - 5 \cdot 0$

Step 2.2.2

Remove parentheses.

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

Step 2.2.3

Simplify $2 {(0)}^{2} - 5 \cdot 0$ .

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

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

$y = 2 \cdot 0 - 5 \cdot 0$

Step 2.2.3.1.2

Multiply $2$ by $0$ .

$y = 0 - 5 \cdot 0$

Step 2.2.3.1.3

Multiply $- 5$ by $0$ .

$y = 0 + 0$

Step 2.2.3.2

Add $0$ and $0$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (\frac{5}{2}, 0)$

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

Step 4