Precalculus Examples

$5.152 x^{3} - 143 x^{2} + 1102 x - 1673$

Step 1

Write $5.152 x^{3} - 143 x^{2} + 1102 x - 1673$ as an equation.

$y = 5.152 x^{3} - 143 x^{2} + 1102 x - 1673$

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 $x$ .

$0 = 5.152 x^{3} - 143 x^{2} + 1102 x - 1673$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$0 = 5.152 x^{3} - 143 x^{2} + 1102 x - 1673$

Step 2.2.2

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

$x \approx 1.99963505, 11.01911072, 14.7374654$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(1.99963505, 0), (11.01911072, 0), (14.7374654, 0)$

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 $y$ .

$y = 5.152 {(0)}^{3} - 143 {(0)}^{2} + 1102 (0) - 1673$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = 5.152 \cdot 0^{3} - 143 {(0)}^{2} + 1102 (0) - 1673$

Step 3.2.2

Remove parentheses.

$y = 5.152 \cdot 0^{3} - 143 \cdot 0^{2} + 1102 (0) - 1673$

Step 3.2.3

Remove parentheses.

$y = 5.152 {(0)}^{3} - 143 {(0)}^{2} + 1102 (0) - 1673$

Step 3.2.4

Simplify $5.152 {(0)}^{3} - 143 {(0)}^{2} + 1102 (0) - 1673$ .

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Step 3.2.4.1

Simplify each term.

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Step 3.2.4.1.1

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

$y = 5.152 \cdot 0 - 143 {(0)}^{2} + 1102 (0) - 1673$

Step 3.2.4.1.2

Multiply $5.152$ by $0$ .

$y = 0 - 143 {(0)}^{2} + 1102 (0) - 1673$

Step 3.2.4.1.3

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

$y = 0 - 143 \cdot 0 + 1102 (0) - 1673$

Step 3.2.4.1.4

Multiply $- 143$ by $0$ .

$y = 0 + 0 + 1102 (0) - 1673$

Step 3.2.4.1.5

Multiply $1102$ by $0$ .

$y = 0 + 0 + 0 - 1673$

Step 3.2.4.2

Simplify by adding and subtracting.

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Step 3.2.4.2.1

Add $0$ and $0$ .

$y = 0 + 0 - 1673$

Step 3.2.4.2.2

Add $0$ and $0$ .

$y = 0 - 1673$

Step 3.2.4.2.3

Subtract $1673$ from $0$ .

$y = - 1673$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 1673)$

Step 4

List the intersections.

x-intercept(s): $(1.99963505, 0), (11.01911072, 0), (14.7374654, 0)$

y-intercept(s): $(0, - 1673)$

Step 5