Find the x and y Intercepts f(x)=-x^4+x^3-6x^2+8x-16

$f (x) = - x^{4} + x^{3} - 6 x^{2} + 8 x - 16$

Find the x-intercepts.

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

$0 = - x^{4} + x^{3} - 6 x^{2} + 8 x - 16$

Solve the equation.

Remove parentheses.

$0 = - x^{4} + x^{3} - 6 x^{2} + 8 x - 16$

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

No solution

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = - {(0)}^{4} + {(0)}^{3} - 6 {(0)}^{2} + 8 (0) - 16$

Solve the equation.

Remove parentheses.

$y = - 0^{4} + {(0)}^{3} - 6 {(0)}^{2} + 8 (0) - 16$

Remove parentheses.

$y = - 0^{4} + 0^{3} - 6 {(0)}^{2} + 8 (0) - 16$

Remove parentheses.

$y = - 0^{4} + 0^{3} - 6 \cdot 0^{2} + 8 (0) - 16$

Remove parentheses.

$y = - {(0)}^{4} + {(0)}^{3} - 6 {(0)}^{2} + 8 (0) - 16$

Simplify $- {(0)}^{4} + {(0)}^{3} - 6 {(0)}^{2} + 8 (0) - 16$ .

Simplify each term.

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

$y = - 0 + {(0)}^{3} - 6 {(0)}^{2} + 8 (0) - 16$

Multiply $- 1$ by $0$ .

$y = 0 + {(0)}^{3} - 6 {(0)}^{2} + 8 (0) - 16$

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

$y = 0 + 0 - 6 {(0)}^{2} + 8 (0) - 16$

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

$y = 0 + 0 - 6 \cdot 0 + 8 (0) - 16$

Multiply $- 6$ by $0$ .

$y = 0 + 0 + 0 + 8 (0) - 16$

Multiply $8$ by $0$ .

$y = 0 + 0 + 0 + 0 - 16$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 + 0 + 0 - 16$

Add $0$ and $0$ .

$y = 0 + 0 - 16$

Add $0$ and $0$ .

$y = 0 - 16$

Subtract $16$ from $0$ .

$y = - 16$

y-intercept(s) in point form.

y-intercept(s): $(0, - 16)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - 16)$

Find the x and y Intercepts f(x)=-x^4+x^3-6x^2+8x-16

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