Find the x and y Intercepts f(x)=x^2-49

$f (x) = x^{2} - 49$

Step 1

Find the x-intercepts.

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

$0 = x^{2} - 49$

Solve the equation.

Rewrite the equation as $x^{2} - 49 = 0$ .

$x^{2} - 49 = 0$

Add $49$ to both sides of the equation.

$x^{2} = 49$

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

$x = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2}}$

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

$x = \pm 7$

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.

$x = 7$

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

$x = - 7$

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

$x = 7, - 7$

x-intercept(s) in point form.

x-intercept(s): $(7, 0), (- 7, 0)$

Step 2

Find the y-intercepts.

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

$y = {(0)}^{2} - 49$

Solve the equation.

Remove parentheses.

$y = 0^{2} - 49$

Remove parentheses.

$y = {(0)}^{2} - 49$

Simplify ${(0)}^{2} - 49$ .

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

$y = 0 - 49$

Subtract $49$ from $0$ .

$y = - 49$

y-intercept(s) in point form.

y-intercept(s): $(0, - 49)$

Step 3

List the intersections.

x-intercept(s): $(7, 0), (- 7, 0)$

y-intercept(s): $(0, - 49)$

Step 4

Find the x and y Intercepts f(x)=x^2-49

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