Find the x and y Intercepts y=16-x^2

$y = 16 - x^{2}$

Step 1

Find the x-intercepts.

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

$0 = 16 - x^{2}$

Solve the equation.

Rewrite the equation as $16 - x^{2} = 0$ .

$16 - x^{2} = 0$

Subtract $16$ from both sides of the equation.

$- x^{2} = - 16$

Divide each term in $- x^{2} = - 16$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 16$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 16}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 16}{- 1}$

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

$x^{2} = \frac{- 16}{- 1}$

Simplify the right side.

Divide $- 16$ by $- 1$ .

$x^{2} = 16$

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

$x = \pm \sqrt{16}$

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

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

$x = \pm 4$

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.

$x = 4$

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

$x = - 4$

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

$x = 4, - 4$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (- 4, 0)$

Step 2

Find the y-intercepts.

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

$y = 16 - {(0)}^{2}$

Solve the equation.

Remove parentheses.

$y = 16 - 0^{2}$

Remove parentheses.

$y = 16 - {(0)}^{2}$

Simplify $16 - {(0)}^{2}$ .

Simplify each term.

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

$y = 16 - 0$

Multiply $- 1$ by $0$ .

$y = 16 + 0$

Add $16$ and $0$ .

$y = 16$

y-intercept(s) in point form.

y-intercept(s): $(0, 16)$

Step 3

List the intersections.

x-intercept(s): $(4, 0), (- 4, 0)$

y-intercept(s): $(0, 16)$

Step 4

Find the x and y Intercepts y=16-x^2

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