Find the x and y Intercepts f(x)=-3 square root of -2x-3

$f (x) = - 3 \sqrt{- 2 x - 3}$

Step 1

Find the x-intercepts.

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

$0 = - 3 \sqrt{- 2 x - 3}$

Solve the equation.

Rewrite the equation as $- 3 \sqrt{- 2 x - 3} = 0$ .

$- 3 \sqrt{- 2 x - 3} = 0$

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

${(- 3 \sqrt{- 2 x - 3})}^{2} = 0^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{- 2 x - 3}$ as ${(- 2 x - 3)}^{\frac{1}{2}}$ .

${(- 3 {(- 2 x - 3)}^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the left side.

Simplify ${(- 3 {(- 2 x - 3)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 3 {(- 2 x - 3)}^{\frac{1}{2}}$ .

${(- 3)}^{2} {({(- 2 x - 3)}^{\frac{1}{2}})}^{2} = 0^{2}$

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

$9 {({(- 2 x - 3)}^{\frac{1}{2}})}^{2} = 0^{2}$

Multiply the exponents in ${({(- 2 x - 3)}^{\frac{1}{2}})}^{2}$ .

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

$9 {(- 2 x - 3)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 {(- 2 x - 3)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

$9 {(- 2 x - 3)}^{1} = 0^{2}$

Simplify.

$9 (- 2 x - 3) = 0^{2}$

Apply the distributive property.

$9 (- 2 x) + 9 \cdot - 3 = 0^{2}$

Multiply.

Multiply $- 2$ by $9$ .

$- 18 x + 9 \cdot - 3 = 0^{2}$

Multiply $9$ by $- 3$ .

$- 18 x - 27 = 0^{2}$

Simplify the right side.

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

$- 18 x - 27 = 0$

Solve for $x$ .

Add $27$ to both sides of the equation.

$- 18 x = 27$

Divide each term in $- 18 x = 27$ by $- 18$ and simplify.

Divide each term in $- 18 x = 27$ by $- 18$ .

$\frac{- 18 x}{- 18} = \frac{27}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 x}{- 18} = \frac{27}{- 18}$

Divide $x$ by $1$ .

$x = \frac{27}{- 18}$

Simplify the right side.

Cancel the common factor of $27$ and $- 18$ .

Factor $9$ out of $27$ .

$x = \frac{9 (3)}{- 18}$

Cancel the common factors.

Factor $9$ out of $- 18$ .

$x = \frac{9 \cdot 3}{9 \cdot - 2}$

Cancel the common factor.

$x = \frac{9 \cdot 3}{9 \cdot - 2}$

Rewrite the expression.

$x = \frac{3}{- 2}$

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{3}{2}, 0)$

Step 2

Find the y-intercepts.

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

$y = - 3 \sqrt{- 2 \cdot 0 - 3}$

Simplify $- 3 \sqrt{- 2 \cdot 0 - 3}$ .

Simplify the expression.

Multiply $- 2$ by $0$ .

$y = - 3 \sqrt{0 - 3}$

Subtract $3$ from $0$ .

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

Rewrite $- 3$ as $- 1 (3)$ .

$y = - 3 \sqrt{- 1 (3)}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$y = - 3 (\sqrt{- 1} \cdot \sqrt{3})$

Rewrite $\sqrt{- 1}$ as $i$ .

$y = - 3 i \sqrt{3}$

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

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(- \frac{3}{2}, 0)$

y-intercept(s): $None$

Step 4

Find the x and y Intercepts f(x)=-3 square root of -2x-3

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