Find the x and y Intercepts y=-1/5(x-5)^2-2

$y = - \frac{1}{5} {(x - 5)}^{2} - 2$

Find the x-intercepts.

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

$0 = - \frac{1}{5} \cdot {(x - 5)}^{2} - 2$

Solve the equation.

Rewrite the equation as $- \frac{1}{5} \cdot {(x - 5)}^{2} - 2 = 0$ .

$- \frac{1}{5} \cdot {(x - 5)}^{2} - 2 = 0$

Add $2$ to both sides of the equation.

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

Combine ${(x - 5)}^{2}$ and $\frac{1}{5}$ .

$- \frac{{(x - 5)}^{2}}{5} = 2$

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{{(x - 5)}^{2}}{5}) = - 5 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{{(x - 5)}^{2}}{5}$ into the numerator.

$- 5 \frac{- {(x - 5)}^{2}}{5} = - 5 \cdot 2$

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 {(x - 5)}^{2} = - 5 \cdot 2$

Multiply ${(x - 5)}^{2}$ by $1$ .

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

Simplify the right side.

Multiply $- 5$ by $2$ .

${(x - 5)}^{2} = - 10$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x - 5 = \pm \sqrt{- 10}$

Simplify $\pm \sqrt{- 10}$ .

Rewrite $- 10$ as $- 1 (10)$ .

$x - 5 = \pm \sqrt{- 1 (10)}$

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$x - 5 = \pm \sqrt{- 1} \cdot \sqrt{10}$

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

$x - 5 = \pm i \sqrt{10}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x - 5 = i \sqrt{10}$

Add $5$ to both sides of the equation.

$x = i \sqrt{10} + 5$

Next, use the negative value of the $\pm$ to find the second solution.

$x - 5 = - i \sqrt{10}$

Add $5$ to both sides of the equation.

$x = - i \sqrt{10} + 5$

The complete solution is the result of both the positive and negative portions of the solution.

$x = i \sqrt{10} + 5, - i \sqrt{10} + 5$

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = - \frac{1}{5} \cdot {((0) - 5)}^{2} - 2$

Solve the equation.

Remove parentheses.

$y = - \frac{1}{5} \cdot {(0 - 5)}^{2} - 2$

Remove parentheses.

$y = - \frac{1}{5} \cdot {((0) - 5)}^{2} - 2$

Simplify $- \frac{1}{5} \cdot {((0) - 5)}^{2} - 2$ .

Simplify each term.

Subtract $5$ from $0$ .

$y = - \frac{1}{5} \cdot {(- 5)}^{2} - 2$

Raise $- 5$ to the power of $2$ .

$y = - \frac{1}{5} \cdot 25 - 2$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$y = \frac{- 1}{5} \cdot 25 - 2$

Factor $5$ out of $25$ .

$y = \frac{- 1}{5} \cdot (5 (5)) - 2$

Cancel the common factor.

$y = \frac{- 1}{5} \cdot (5 \cdot 5) - 2$

Rewrite the expression.

$y = - 1 \cdot 5 - 2$

Multiply $- 1$ by $5$ .

$y = - 5 - 2$

Subtract $2$ from $- 5$ .

$y = - 7$

y-intercept(s) in point form.

y-intercept(s): $(0, - 7)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - 7)$

Find the x and y Intercepts y=-1/5(x-5)^2-2

Related Questions

Support LCMGCF.com by disabling your adblocker.