Algebra Examples

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

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = - \frac{1}{2} \cdot \sqrt{x}$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

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

$- \frac{1}{2} \cdot \sqrt{x} = 0$

Step 1.2.2

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{1}{2} \cdot \sqrt{x}) = - 2 \cdot 0$

Step 1.2.3

Simplify both sides of the equation.

Tap for more steps...

Step 1.2.3.1

Simplify the left side.

Tap for more steps...

Step 1.2.3.1.1

Simplify $- 2 (- \frac{1}{2} \cdot \sqrt{x})$ .

Tap for more steps...

Step 1.2.3.1.1.1

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

$- 2 (- \frac{\sqrt{x}}{2}) = - 2 \cdot 0$

Step 1.2.3.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.3.1.1.2.1

Move the leading negative in $- \frac{\sqrt{x}}{2}$ into the numerator.

$- 2 \frac{- \sqrt{x}}{2} = - 2 \cdot 0$

Step 1.2.3.1.1.2.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- \sqrt{x}}{2} = - 2 \cdot 0$

Step 1.2.3.1.1.2.3

Cancel the common factor.

$2 \cdot - 1 \frac{- \sqrt{x}}{2} = - 2 \cdot 0$

Step 1.2.3.1.1.2.4

Rewrite the expression.

$- - \sqrt{x} = - 2 \cdot 0$

Step 1.2.3.1.1.3

Multiply.

Tap for more steps...

Step 1.2.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 \sqrt{x} = - 2 \cdot 0$

Step 1.2.3.1.1.3.2

Multiply $\sqrt{x}$ by $1$ .

$\sqrt{x} = - 2 \cdot 0$

Step 1.2.3.2

Simplify the right side.

Tap for more steps...

Step 1.2.3.2.1

Multiply $- 2$ by $0$ .

$\sqrt{x} = 0$

Step 1.2.4

To remove the radical on the left side of the equation, square both sides of the equation.

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

Step 1.2.5

Simplify each side of the equation.

Tap for more steps...

Step 1.2.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = 0^{2}$

Step 1.2.5.2

Simplify the left side.

Tap for more steps...

Step 1.2.5.2.1

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 1.2.5.2.1.1

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 1.2.5.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 1.2.5.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.5.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 1.2.5.2.1.1.2.2

Rewrite the expression.

$x^{1} = 0^{2}$

Step 1.2.5.2.1.2

Simplify.

$x = 0^{2}$

Step 1.2.5.3

Simplify the right side.

Tap for more steps...

Step 1.2.5.3.1

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

$x = 0$

Step 1.3

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

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

Step 2.2

Simplify $- \frac{1}{2} \cdot \sqrt{0}$ .

Tap for more steps...

Step 2.2.1

Remove parentheses.

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Multiply $- \frac{1}{2} \cdot 0$ .

Tap for more steps...

Step 2.2.4.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{1}{2})$

Step 2.2.4.2

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

$y = 0$

Step 2.3

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