Calculus Examples

$y = x^{5} - 5 x^{4} + 20 x^{2}$

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 $x$ .

$0 = x^{5} - 5 x^{4} + 20 x^{2}$

Step 1.2

Solve the equation.

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Step 1.2.1

Remove parentheses.

$0 = x^{5} - 5 x^{4} + 20 x^{2}$

Step 1.2.2

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

$x \approx - 1.72457672, 0$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 1.72457672, 0), (0, 0)$

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 $y$ .

$y = {(0)}^{5} - 5 {(0)}^{4} + 20 {(0)}^{2}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 0^{5} - 5 {(0)}^{4} + 20 {(0)}^{2}$

Step 2.2.2

Remove parentheses.

$y = 0^{5} - 5 \cdot 0^{4} + 20 {(0)}^{2}$

Step 2.2.3

Remove parentheses.

$y = 0^{5} - 5 \cdot 0^{4} + 20 \cdot 0^{2}$

Step 2.2.4

Remove parentheses.

$y = {(0)}^{5} - 5 {(0)}^{4} + 20 {(0)}^{2}$

Step 2.2.5

Simplify ${(0)}^{5} - 5 {(0)}^{4} + 20 {(0)}^{2}$ .

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Step 2.2.5.1

Simplify each term.

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Step 2.2.5.1.1

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

$y = 0 - 5 {(0)}^{4} + 20 {(0)}^{2}$

Step 2.2.5.1.2

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

$y = 0 - 5 \cdot 0 + 20 {(0)}^{2}$

Step 2.2.5.1.3

Multiply $- 5$ by $0$ .

$y = 0 + 0 + 20 {(0)}^{2}$

Step 2.2.5.1.4

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

$y = 0 + 0 + 20 \cdot 0$

Step 2.2.5.1.5

Multiply $20$ by $0$ .

$y = 0 + 0 + 0$

Step 2.2.5.2

Simplify by adding numbers.

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Step 2.2.5.2.1

Add $0$ and $0$ .

$y = 0 + 0$

Step 2.2.5.2.2

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): $(- 1.72457672, 0), (0, 0)$

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

Step 4