Finite Math Examples

$y = 0.2 x^{3} - 23 x^{2} + 1529 x + 34.574$

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 $x$ .

$0 = 0.2 x^{3} - 23 x^{2} + 1529 x + 34.574$

Step 1.2

Solve the equation.

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Step 1.2.1

Remove parentheses.

$0 = 0.2 x^{3} - 23 x^{2} + 1529 x + 34.574$

Step 1.2.2

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

$x \approx - 0.02260447$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 0.02260447, 0)$

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 $y$ .

$y = 0.2 {(0)}^{3} - 23 {(0)}^{2} + 1529 (0) + 34.574$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 0.2 \cdot 0^{3} - 23 {(0)}^{2} + 1529 (0) + 34.574$

Step 2.2.2

Remove parentheses.

$y = 0.2 \cdot 0^{3} - 23 \cdot 0^{2} + 1529 (0) + 34.574$

Step 2.2.3

Remove parentheses.

$y = 0.2 {(0)}^{3} - 23 {(0)}^{2} + 1529 (0) + 34.574$

Step 2.2.4

Simplify $0.2 {(0)}^{3} - 23 {(0)}^{2} + 1529 (0) + 34.574$ .

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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 $0$ .

$y = 0.2 \cdot 0 - 23 {(0)}^{2} + 1529 (0) + 34.574$

Step 2.2.4.1.2

Multiply $0.2$ by $0$ .

$y = 0 - 23 {(0)}^{2} + 1529 (0) + 34.574$

Step 2.2.4.1.3

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

$y = 0 - 23 \cdot 0 + 1529 (0) + 34.574$

Step 2.2.4.1.4

Multiply $- 23$ by $0$ .

$y = 0 + 0 + 1529 (0) + 34.574$

Step 2.2.4.1.5

Multiply $1529$ by $0$ .

$y = 0 + 0 + 0 + 34.574$

Step 2.2.4.2

Simplify by adding numbers.

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Step 2.2.4.2.1

Add $0$ and $0$ .

$y = 0 + 0 + 34.574$

Step 2.2.4.2.2

Add $0$ and $0$ .

$y = 0 + 34.574$

Step 2.2.4.2.3

Add $0$ and $34.574$ .

$y = 34.574$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 34.574)$

Step 3

List the intersections.

x-intercept(s): $(- 0.02260447, 0)$

y-intercept(s): $(0, 34.574)$

Step 4