Find the x and y Intercepts f(x)=1/2x^2-4

$f (x) = \frac{1}{2} x^{2} - 4$

Find the x-intercepts.

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

$0 = \frac{1}{2} x^{2} - 4$

Solve the equation.

Rewrite the equation as $\frac{1}{2} x^{2} - 4 = 0$ .

$\frac{1}{2} x^{2} - 4 = 0$

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

$\frac{x^{2}}{2} - 4 = 0$

Add $4$ to both sides of the equation.

$\frac{x^{2}}{2} = 4$

Multiply both sides of the equation by $2$ .

$2 \frac{x^{2}}{2} = 2 \cdot 4$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x^{2}}{2} = 2 \cdot 4$

Rewrite the expression.

$x^{2} = 2 \cdot 4$

Simplify the right side.

Multiply $2$ by $4$ .

$x^{2} = 8$

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

$x = \pm \sqrt{8}$

Simplify $\pm \sqrt{8}$ .

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$x = \pm \sqrt{4 (2)}$

Rewrite $4$ as $2^{2}$ .

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

Pull terms out from under the radical.

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

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2 \sqrt{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2 \sqrt{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2 \sqrt{2}, - 2 \sqrt{2}$

x-intercept(s) in point form.

x-intercept(s): $(2 \sqrt{2}, 0), (- 2 \sqrt{2}, 0)$

Find the y-intercepts.

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

$y = \frac{1}{2} \cdot {(0)}^{2} - 4$

Solve the equation.

Remove parentheses.

$y = \frac{1}{2} \cdot 0^{2} - 4$

Remove parentheses.

$y = \frac{1}{2} \cdot {(0)}^{2} - 4$

Simplify $\frac{1}{2} \cdot {(0)}^{2} - 4$ .

Simplify each term.

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

$y = \frac{1}{2} \cdot 0 - 4$

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

$y = 0 - 4$

Subtract $4$ from $0$ .

$y = - 4$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

List the intersections.

x-intercept(s): $(2 \sqrt{2}, 0), (- 2 \sqrt{2}, 0)$

y-intercept(s): $(0, - 4)$

Find the x and y Intercepts f(x)=1/2x^2-4

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