Find the x and y Intercepts f(x)=2 square root of x+4

$f (x) = 2 \sqrt{x + 4}$

Step 1

Find the x-intercepts.

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

$0 = 2 \sqrt{x + 4}$

Solve the equation.

Rewrite the equation as $2 \sqrt{x + 4} = 0$ .

$2 \sqrt{x + 4} = 0$

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

${(2 \sqrt{x + 4})}^{2} = 0^{2}$

Simplify each side of the equation.

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

${(2 {(x + 4)}^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the left side.

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

Apply the product rule to $2 {(x + 4)}^{\frac{1}{2}}$ .

$2^{2} {({(x + 4)}^{\frac{1}{2}})}^{2} = 0^{2}$

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

$4 {({(x + 4)}^{\frac{1}{2}})}^{2} = 0^{2}$

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

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

$4 {(x + 4)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(x + 4)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

$4 {(x + 4)}^{1} = 0^{2}$

Simplify.

$4 (x + 4) = 0^{2}$

Apply the distributive property.

$4 x + 4 \cdot 4 = 0^{2}$

Multiply $4$ by $4$ .

$4 x + 16 = 0^{2}$

Simplify the right side.

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

$4 x + 16 = 0$

Solve for $x$ .

Subtract $16$ from both sides of the equation.

$4 x = - 16$

Divide each term in $4 x = - 16$ by $4$ and simplify.

Divide each term in $4 x = - 16$ by $4$ .

$\frac{4 x}{4} = \frac{- 16}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 16}{4}$

Divide $x$ by $1$ .

$x = \frac{- 16}{4}$

Simplify the right side.

Divide $- 16$ by $4$ .

$x = - 4$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = 2 \sqrt{(0) + 4}$

Simplify $2 \sqrt{(0) + 4}$ .

Add $0$ and $4$ .

$y = 2 \sqrt{4}$

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

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

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

$y = 2 \cdot 2$

Multiply $2$ by $2$ .

$y = 4$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts f(x)=2 square root of x+4

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