Find the x and y Intercepts f(x)=-1/2 square root of x

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

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

Simplify both sides of the equation.

Simplify the left side.

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

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

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

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

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

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

Simplify the right side.

Multiply $- 2$ by $0$ .

$\sqrt{x} = 0$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x = 0^{2}$

Simplify the right side.

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

$x = 0$

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 $y$ .

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

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

Remove parentheses.

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

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

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

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

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

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

Multiply $0$ by $- 1$ .

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

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

$y = 0$

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 f(x)=-1/2 square root of x

Related Questions

Support LCMGCF.com by disabling your adblocker.