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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

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

$x \approx 0.54764357$

x-intercept(s) in point form.

x-intercept(s): $(0.54764357, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

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

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

Multiply $- 4$ by $0$ .

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

Multiply $- 3$ by $0$ .

$y = 2 + 0 + 0 + {(0)}^{2}$

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

$y = 2 + 0 + 0 + 0$

Simplify by adding numbers.

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): $(0.54764357, 0)$

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

Step 4

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

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