Find the x and y Intercepts y=1/2x^3+x^2-3x+1

$y = \frac{1}{2} x^{3} + x^{2} - 3 x + 1$

Find the x-intercepts.

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

$0 = \frac{1}{2} x^{3} + x^{2} - 3 x + 1$

Solve the equation.

Remove parentheses.

$0 = \frac{1}{2} x^{3} + x^{2} - 3 x + 1$

Combine $\frac{1}{2}$ and $x^{3}$ .

$0 = \frac{x^{3}}{2} + x^{2} - 3 x + 1$

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

$x \approx - 3.74482607, 0.39593186, 1.34889421$

x-intercept(s) in point form.

x-intercept(s): $(- 3.74482607, 0), (0.39593186, 0), (1.34889421, 0)$

Find the y-intercepts.

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

$y = \frac{1}{2} \cdot {(0)}^{3} + {(0)}^{2} - 3 \cdot 0 + 1$

Solve the equation.

Remove parentheses.

$y = \frac{1}{2} \cdot 0^{3} + {(0)}^{2} - 3 \cdot 0 + 1$

Remove parentheses.

$y = \frac{1}{2} \cdot 0^{3} + 0^{2} - 3 \cdot 0 + 1$

Remove parentheses.

$y = \frac{1}{2} \cdot {(0)}^{3} + {(0)}^{2} - 3 \cdot 0 + 1$

Simplify $\frac{1}{2} \cdot {(0)}^{3} + {(0)}^{2} - 3 \cdot 0 + 1$ .

Simplify each term.

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

$y = \frac{1}{2} \cdot 0 + {(0)}^{2} - 3 \cdot 0 + 1$

Multiply $\frac{1}{2}$ by $0$ .

$y = 0 + {(0)}^{2} - 3 \cdot 0 + 1$

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

$y = 0 + 0 - 3 \cdot 0 + 1$

Multiply $- 3$ by $0$ .

$y = 0 + 0 + 0 + 1$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 0 + 1$

Add $0$ and $0$ .

$y = 0 + 1$

Add $0$ and $1$ .

$y = 1$

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

List the intersections.

x-intercept(s): $(- 3.74482607, 0), (0.39593186, 0), (1.34889421, 0)$

y-intercept(s): $(0, 1)$