Find the x and y Intercepts y=-x^2+2

$y = - x^{2} + 2$

Find the x-intercepts.

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

$0 = - x^{2} + 2$

Solve the equation.

Rewrite the equation as $- x^{2} + 2 = 0$ .

$- x^{2} + 2 = 0$

Subtract $2$ from both sides of the equation.

$- x^{2} = - 2$

Divide each term in $- x^{2} = - 2$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 2$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 2}{- 1}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x^{2} = 2$

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

$x = \pm \sqrt{2}$

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.

$x = \sqrt{2}$

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

$x = - \sqrt{2}$

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

$x = \sqrt{2}, - \sqrt{2}$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = - {(0)}^{2} + 2$

Solve the equation.

Remove parentheses.

$y = - 0^{2} + 2$

Remove parentheses.

$y = - {(0)}^{2} + 2$

Simplify $- {(0)}^{2} + 2$ .

Simplify each term.

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

$y = - 0 + 2$

Multiply $- 1$ by $0$ .

$y = 0 + 2$

Add $0$ and $2$ .

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

List the intersections.

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

y-intercept(s): $(0, 2)$

Find the x and y Intercepts y=-x^2+2

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