Find the x and y Intercepts f(x)=-7x-2-2x^2-2x^4+5x^3

$f (x) = - 7 x - 2 - 2 x^{2} - 2 x^{4} + 5 x^{3}$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - 7 x - 2 - 2 x^{2} - 2 x^{4} + 5 x^{3}$

Solve the equation.

Remove parentheses.

$0 = - 7 x - 2 - 2 x^{2} - 2 x^{4} + 5 x^{3}$

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

$x \approx - 0.64376237, - 0.36188238$

x-intercept(s) in point form.

x-intercept(s): $(- 0.64376237, 0), (- 0.36188238, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - 7 \cdot 0 - 2 - 2 {(0)}^{2} - 2 {(0)}^{4} + 5 {(0)}^{3}$

Solve the equation.

Remove parentheses.

$y = - 7 \cdot 0 - 2 - 2 \cdot 0^{2} - 2 {(0)}^{4} + 5 {(0)}^{3}$

Remove parentheses.

$y = - 7 \cdot 0 - 2 - 2 \cdot 0^{2} - 2 \cdot 0^{4} + 5 {(0)}^{3}$

Remove parentheses.

$y = - 7 \cdot 0 - 2 - 2 \cdot 0^{2} - 2 \cdot 0^{4} + 5 \cdot 0^{3}$

Remove parentheses.

$y = - 7 \cdot 0 - 2 - 2 {(0)}^{2} - 2 {(0)}^{4} + 5 {(0)}^{3}$

Simplify $- 7 \cdot 0 - 2 - 2 {(0)}^{2} - 2 {(0)}^{4} + 5 {(0)}^{3}$ .

Simplify each term.

Multiply $- 7$ by $0$ .

$y = 0 - 2 - 2 {(0)}^{2} - 2 {(0)}^{4} + 5 {(0)}^{3}$

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

$y = 0 - 2 - 2 \cdot 0 - 2 {(0)}^{4} + 5 {(0)}^{3}$

Multiply $- 2$ by $0$ .

$y = 0 - 2 + 0 - 2 {(0)}^{4} + 5 {(0)}^{3}$

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

$y = 0 - 2 + 0 - 2 \cdot 0 + 5 {(0)}^{3}$

Multiply $- 2$ by $0$ .

$y = 0 - 2 + 0 + 0 + 5 {(0)}^{3}$

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

$y = 0 - 2 + 0 + 0 + 5 \cdot 0$

Multiply $5$ by $0$ .

$y = 0 - 2 + 0 + 0 + 0$

Simplify by adding and subtracting.

Subtract $2$ from $0$ .

$y = - 2 + 0 + 0 + 0$

Add $- 2$ and $0$ .

$y = - 2 + 0 + 0$

Add $- 2$ and $0$ .

$y = - 2 + 0$

Add $- 2$ and $0$ .

$y = - 2$

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

Step 3

List the intersections.

x-intercept(s): $(- 0.64376237, 0), (- 0.36188238, 0)$

y-intercept(s): $(0, - 2)$

Step 4

Find the x and y Intercepts f(x)=-7x-2-2x^2-2x^4+5x^3

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