Find the x and y Intercepts y=3/2x^2

$y = \frac{3}{2} x^{2}$

Step 1

Find the x-intercepts.

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

$0 = \frac{3}{2} x^{2}$

Solve the equation.

Rewrite the equation as $\frac{3}{2} x^{2} = 0$ .

$\frac{3}{2} x^{2} = 0$

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} (\frac{3}{2} x^{2}) = \frac{2}{3} \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} (\frac{3}{2} x^{2})$ .

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

$\frac{2}{3} \cdot \frac{3 x^{2}}{2} = \frac{2}{3} \cdot 0$

Combine.

$\frac{2 (3 x^{2})}{3 \cdot 2} = \frac{2}{3} \cdot 0$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (3 x^{2})}{3 \cdot 2} = \frac{2}{3} \cdot 0$

Rewrite the expression.

$\frac{3 x^{2}}{3} = \frac{2}{3} \cdot 0$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{2}{3} \cdot 0$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{2}{3} \cdot 0$

Simplify the right side.

Multiply $\frac{2}{3}$ by $0$ .

$x^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

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

$y = \frac{3}{2} \cdot 0$

Multiply $\frac{3}{2}$ by $0$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts y=3/2x^2

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