Find the x and y Intercepts f(x)=-5x-9+4x^2+5x^3

$f (x) = - 5 x - 9 + 4 x^{2} + 5 x^{3}$

Step 1

Find the x-intercepts.

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

$0 = - 5 x - 9 + 4 x^{2} + 5 x^{3}$

Solve the equation.

Remove parentheses.

$0 = - 5 x - 9 + 4 x^{2} + 5 x^{3}$

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

$x \approx 1.22247446$

x-intercept(s) in point form.

x-intercept(s): $(1.22247446, 0)$

Step 2

Find the y-intercepts.

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

$y = - 5 \cdot 0 - 9 + 4 {(0)}^{2} + 5 {(0)}^{3}$

Solve the equation.

Remove parentheses.

$y = - 5 \cdot 0 - 9 + 4 \cdot 0^{2} + 5 {(0)}^{3}$

Remove parentheses.

$y = - 5 \cdot 0 - 9 + 4 \cdot 0^{2} + 5 \cdot 0^{3}$

Remove parentheses.

$y = - 5 \cdot 0 - 9 + 4 {(0)}^{2} + 5 {(0)}^{3}$

Simplify $- 5 \cdot 0 - 9 + 4 {(0)}^{2} + 5 {(0)}^{3}$ .

Simplify each term.

Multiply $- 5$ by $0$ .

$y = 0 - 9 + 4 {(0)}^{2} + 5 {(0)}^{3}$

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

$y = 0 - 9 + 4 \cdot 0 + 5 {(0)}^{3}$

Multiply $4$ by $0$ .

$y = 0 - 9 + 0 + 5 {(0)}^{3}$

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

$y = 0 - 9 + 0 + 5 \cdot 0$

Multiply $5$ by $0$ .

$y = 0 - 9 + 0 + 0$

Simplify by adding and subtracting.

Subtract $9$ from $0$ .

$y = - 9 + 0 + 0$

Add $- 9$ and $0$ .

$y = - 9 + 0$

Add $- 9$ and $0$ .

$y = - 9$

y-intercept(s) in point form.

y-intercept(s): $(0, - 9)$

Step 3

List the intersections.

x-intercept(s): $(1.22247446, 0)$

y-intercept(s): $(0, - 9)$

Step 4

Find the x and y Intercepts f(x)=-5x-9+4x^2+5x^3

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