Find the x and y Intercepts y=8-x^2

$y = 8 - x^{2}$

Step 1

Find the x-intercepts.

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

$0 = 8 - x^{2}$

Solve the equation.

Rewrite the equation as $8 - x^{2} = 0$ .

$8 - x^{2} = 0$

Subtract $8$ from both sides of the equation.

$- x^{2} = - 8$

Divide each term in $- x^{2} = - 8$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 8$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 8}{- 1}$

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

$x^{2} = \frac{- 8}{- 1}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$x^{2} = 8$

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

$x = \pm \sqrt{8}$

Simplify $\pm \sqrt{8}$ .

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$x = \pm \sqrt{4 (2)}$

Rewrite $4$ as $2^{2}$ .

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

Pull terms out from under the radical.

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

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.

$x = 2 \sqrt{2}$

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

$x = - 2 \sqrt{2}$

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

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

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = 8 - {(0)}^{2}$

Solve the equation.

Remove parentheses.

$y = 8 - 0^{2}$

Remove parentheses.

$y = 8 - {(0)}^{2}$

Simplify $8 - {(0)}^{2}$ .

Simplify each term.

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

$y = 8 - 0$

Multiply $- 1$ by $0$ .

$y = 8 + 0$

Add $8$ and $0$ .

$y = 8$

y-intercept(s) in point form.

y-intercept(s): $(0, 8)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 8)$

Step 4

Find the x and y Intercepts y=8-x^2

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