Finite Math Examples

$f (x) = 6 x^{4} - 18 x - 318 x^{3} - 54 x$

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 $x$ .

$0 = 6 x^{4} - 18 x - 318 x^{3} - 54 x$

Step 1.2

Solve the equation.

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Step 1.2.1

Remove parentheses.

$0 = 6 x^{4} - 18 x - 318 x^{3} - 54 x$

Step 1.2.2

Subtract $54 x$ from $- 18 x$ .

$0 = 6 x^{4} - 318 x^{3} - 72 x$

Step 1.2.3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 0$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$y = 6 {(0)}^{4} - 18 \cdot 0 - 318 {(0)}^{3} - 54 \cdot 0$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 6 \cdot 0^{4} - 18 \cdot 0 - 318 {(0)}^{3} - 54 \cdot 0$

Step 2.2.2

Remove parentheses.

$y = 6 \cdot 0^{4} - 18 \cdot 0 - 318 \cdot 0^{3} - 54 \cdot 0$

Step 2.2.3

Remove parentheses.

$y = 6 {(0)}^{4} - 18 \cdot 0 - 318 {(0)}^{3} - 54 \cdot 0$

Step 2.2.4

Simplify $6 {(0)}^{4} - 18 \cdot 0 - 318 {(0)}^{3} - 54 \cdot 0$ .

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Step 2.2.4.1

Simplify each term.

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Step 2.2.4.1.1

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

$y = 6 \cdot 0 - 18 \cdot 0 - 318 {(0)}^{3} - 54 \cdot 0$

Step 2.2.4.1.2

Multiply $6$ by $0$ .

$y = 0 - 18 \cdot 0 - 318 {(0)}^{3} - 54 \cdot 0$

Step 2.2.4.1.3

Multiply $- 18$ by $0$ .

$y = 0 + 0 - 318 {(0)}^{3} - 54 \cdot 0$

Step 2.2.4.1.4

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

$y = 0 + 0 - 318 \cdot 0 - 54 \cdot 0$

Step 2.2.4.1.5

Multiply $- 318$ by $0$ .

$y = 0 + 0 + 0 - 54 \cdot 0$

Step 2.2.4.1.6

Multiply $- 54$ by $0$ .

$y = 0 + 0 + 0 + 0$

Step 2.2.4.2

Simplify by adding numbers.

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Step 2.2.4.2.1

Add $0$ and $0$ .

$y = 0 + 0 + 0$

Step 2.2.4.2.2

Add $0$ and $0$ .

$y = 0 + 0$

Step 2.2.4.2.3

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): $(0, 0)$

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

Step 4