Find the x and y Intercepts f(x)=-4 square root of x+5+6

$f (x) = - 4 \sqrt{x + 5} + 6$

Find the x-intercepts.

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

$0 = - 4 \sqrt{x + 5} + 6$

Solve the equation.

Rewrite the equation as $- 4 \sqrt{x + 5} + 6 = 0$ .

$- 4 \sqrt{x + 5} + 6 = 0$

Subtract $6$ from both sides of the equation.

$- 4 \sqrt{x + 5} = - 6$

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

${(- 4 \sqrt{x + 5})}^{2} = {(- 6)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 5}$ as ${(x + 5)}^{\frac{1}{2}}$ .

${(- 4 {(x + 5)}^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Simplify the left side.

Simplify ${(- 4 {(x + 5)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 4 {(x + 5)}^{\frac{1}{2}}$ .

${(- 4)}^{2} {({(x + 5)}^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Raise $- 4$ to the power of $2$ .

$16 {({(x + 5)}^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Multiply the exponents in ${({(x + 5)}^{\frac{1}{2}})}^{2}$ .

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

$16 {(x + 5)}^{\frac{1}{2} \cdot 2} = {(- 6)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 {(x + 5)}^{\frac{1}{2} \cdot 2} = {(- 6)}^{2}$

Rewrite the expression.

$16 {(x + 5)}^{1} = {(- 6)}^{2}$

Simplify.

$16 (x + 5) = {(- 6)}^{2}$

Apply the distributive property.

$16 x + 16 \cdot 5 = {(- 6)}^{2}$

Multiply $16$ by $5$ .

$16 x + 80 = {(- 6)}^{2}$

Simplify the right side.

Raise $- 6$ to the power of $2$ .

$16 x + 80 = 36$

Solve for $x$ .

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

Subtract $80$ from both sides of the equation.

$16 x = 36 - 80$

Subtract $80$ from $36$ .

$16 x = - 44$

Divide each term in $16 x = - 44$ by $16$ and simplify.

Divide each term in $16 x = - 44$ by $16$ .

$\frac{16 x}{16} = \frac{- 44}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{- 44}{16}$

Divide $x$ by $1$ .

$x = \frac{- 44}{16}$

Simplify the right side.

Cancel the common factor of $- 44$ and $16$ .

Factor $4$ out of $- 44$ .

$x = \frac{4 (- 11)}{16}$

Cancel the common factors.

Factor $4$ out of $16$ .

$x = \frac{4 \cdot - 11}{4 \cdot 4}$

Cancel the common factor.

$x = \frac{4 \cdot - 11}{4 \cdot 4}$

Rewrite the expression.

$x = \frac{- 11}{4}$

Move the negative in front of the fraction.

$x = - \frac{11}{4}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{11}{4}, 0)$

Find the y-intercepts.

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

$y = - 4 \sqrt{(0) + 5} + 6$

Add $0$ and $5$ .

$y = - 4 \sqrt{5} + 6$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4 \sqrt{5} + 6)$

List the intersections.

x-intercept(s): $(- \frac{11}{4}, 0)$

y-intercept(s): $(0, - 4 \sqrt{5} + 6)$

Find the x and y Intercepts f(x)=-4 square root of x+5+6

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