Find the x and y Intercepts square root of x+4-3

$\sqrt{x + 4} - 3$

Step 1

Write $\sqrt{x + 4} - 3$ as an equation.

$y = \sqrt{x + 4} - 3$

Step 2

Find the x-intercepts.

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

$0 = \sqrt{x + 4} - 3$

Solve the equation.

Rewrite the equation as $\sqrt{x + 4} - 3 = 0$ .

$\sqrt{x + 4} - 3 = 0$

Add $3$ to both sides of the equation.

$\sqrt{x + 4} = 3$

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

${\sqrt{x + 4}}^{2} = 3^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 4}$ as ${(x + 4)}^{\frac{1}{2}}$ .

${({(x + 4)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(x + 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x + 4)}^{\frac{1}{2}})}^{2}$ .

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

${(x + 4)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 4)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(x + 4)}^{1} = 3^{2}$

Simplify.

$x + 4 = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$x + 4 = 9$

Move all terms not containing $x$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$x = 9 - 4$

Subtract $4$ from $9$ .

$x = 5$

x-intercept(s) in point form.

x-intercept(s): $(5, 0)$

Step 3

Find the y-intercepts.

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

$y = \sqrt{(0) + 4} - 3$

Simplify $\sqrt{(0) + 4} - 3$ .

Simplify each term.

Add $0$ and $4$ .

$y = \sqrt{4} - 3$

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

$y = \sqrt{2^{2}} - 3$

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

$y = 2 - 3$

Subtract $3$ from $2$ .

$y = - 1$

y-intercept(s) in point form.

y-intercept(s): $(0, - 1)$

Step 4

List the intersections.

x-intercept(s): $(5, 0)$

y-intercept(s): $(0, - 1)$

Step 5

Find the x and y Intercepts square root of x+4-3

Related Questions

Support LCMGCF.com by disabling your adblocker.