Find the x and y Intercepts f(x)=x^2-81

$f (x) = x^{2} - 81$

Step 1

Find the x-intercepts.

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

$0 = x^{2} - 81$

Solve the equation.

Rewrite the equation as $x^{2} - 81 = 0$ .

$x^{2} - 81 = 0$

Add $81$ to both sides of the equation.

$x^{2} = 81$

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

$x = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$x = \pm \sqrt{9^{2}}$

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

$x = \pm 9$

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.

$x = 9$

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

$x = - 9$

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

$x = 9, - 9$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = {(0)}^{2} - 81$

Solve the equation.

Remove parentheses.

$y = 0^{2} - 81$

Remove parentheses.

$y = {(0)}^{2} - 81$

Simplify ${(0)}^{2} - 81$ .

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

$y = 0 - 81$

Subtract $81$ from $0$ .

$y = - 81$

y-intercept(s) in point form.

y-intercept(s): $(0, - 81)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 81)$

Step 4

Find the x and y Intercepts f(x)=x^2-81

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