Algebra Examples

$f (x) = - 4 x^{2} - 2 x^{6} - x^{5} - 7 x^{4}$

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 $x$ .

$0 = - 4 x^{2} - 2 x^{6} - x^{5} - 7 x^{4}$

Step 1.2

Solve the equation.

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Step 1.2.1

Remove parentheses.

$0 = - 4 x^{2} - 2 x^{6} - x^{5} - 7 x^{4}$

Step 1.2.2

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 $y$ .

$y = - 4 {(0)}^{2} - 2 {(0)}^{6} - {(0)}^{5} - 7 {(0)}^{4}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = - 4 \cdot 0^{2} - 2 {(0)}^{6} - {(0)}^{5} - 7 {(0)}^{4}$

Step 2.2.2

Remove parentheses.

$y = - 4 \cdot 0^{2} - 2 \cdot 0^{6} - {(0)}^{5} - 7 {(0)}^{4}$

Step 2.2.3

Remove parentheses.

$y = - 4 \cdot 0^{2} - 2 \cdot 0^{6} - 0^{5} - 7 {(0)}^{4}$

Step 2.2.4

Remove parentheses.

$y = - 4 \cdot 0^{2} - 2 \cdot 0^{6} - 0^{5} - 7 \cdot 0^{4}$

Step 2.2.5

Remove parentheses.

$y = - 4 {(0)}^{2} - 2 {(0)}^{6} - {(0)}^{5} - 7 {(0)}^{4}$

Step 2.2.6

Simplify $- 4 {(0)}^{2} - 2 {(0)}^{6} - {(0)}^{5} - 7 {(0)}^{4}$ .

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Step 2.2.6.1

Simplify each term.

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Step 2.2.6.1.1

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

$y = - 4 \cdot 0 - 2 {(0)}^{6} - {(0)}^{5} - 7 {(0)}^{4}$

Step 2.2.6.1.2

Multiply $- 4$ by $0$ .

$y = 0 - 2 {(0)}^{6} - {(0)}^{5} - 7 {(0)}^{4}$

Step 2.2.6.1.3

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

$y = 0 - 2 \cdot 0 - {(0)}^{5} - 7 {(0)}^{4}$

Step 2.2.6.1.4

Multiply $- 2$ by $0$ .

$y = 0 + 0 - {(0)}^{5} - 7 {(0)}^{4}$

Step 2.2.6.1.5

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

$y = 0 + 0 - 0 - 7 {(0)}^{4}$

Step 2.2.6.1.6

Multiply $- 1$ by $0$ .

$y = 0 + 0 + 0 - 7 {(0)}^{4}$

Step 2.2.6.1.7

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

$y = 0 + 0 + 0 - 7 \cdot 0$

Step 2.2.6.1.8

Multiply $- 7$ by $0$ .

$y = 0 + 0 + 0 + 0$

Step 2.2.6.2

Simplify by adding numbers.

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Step 2.2.6.2.1

Add $0$ and $0$ .

$y = 0 + 0 + 0$

Step 2.2.6.2.2

Add $0$ and $0$ .

$y = 0 + 0$

Step 2.2.6.2.3

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