Find the X and Y Intercepts y=-x^2+9

$y = - x^{2} + 9$

Find the x-intercepts.

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

$0 = - x^{2} + 9$

Solve the equation.

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Rewrite the equation as $- x^{2} + 9 = 0$ .

$- x^{2} + 9 = 0$

Subtract $9$ from both sides of the equation.

$- x^{2} = - 9$

Multiply each term in $- x^{2} = - 9$ by $- 1$

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Multiply each term in $- x^{2} = - 9$ by $- 1$ .

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

Multiply $(- x^{2}) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

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

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

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

Multiply $- 9$ by $- 1$ .

$x^{2} = 9$

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

$x = \pm \sqrt{9}$

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

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Simplify the right side of the equation.

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Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

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

$x = \pm 3$

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

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

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 3, 0)$

Find the y-intercepts.

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

$y = - {(0)}^{2} + 9$

Solve the equation.

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Remove parentheses.

$y = - {(0)}^{2} + 9$

Simplify $- {(0)}^{2} + 9$ .

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Simplify each term.

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

$y = - 0 + 9$

Multiply $- 1$ by $0$ .

$y = 0 + 9$

Add $0$ and $9$ .

$y = 9$

y-intercept(s) in point form.

y-intercept(s): $(0, 9)$

List the intersections.

x-intercept(s): $(3, 0), (- 3, 0)$

y-intercept(s): $(0, 9)$

Find the X and Y Intercepts y=-x^2+9

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