Find the x and y Intercepts f(x)=(x-4)^2-9

$f (x) = {(x - 4)}^{2} - 9$

Step 1

Find the x-intercepts.

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

$0 = {(x - 4)}^{2} - 9$

Solve the equation.

Rewrite the equation as ${(x - 4)}^{2} - 9 = 0$ .

${(x - 4)}^{2} - 9 = 0$

Add $9$ to both sides of the equation.

${(x - 4)}^{2} = 9$

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

$x - 4 = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

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

$x - 4 = \pm \sqrt{3^{2}}$

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

$x - 4 = \pm 3$

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.

$x - 4 = 3$

Move all terms not containing $x$ to the right side of the equation.

Add $4$ to both sides of the equation.

$x = 3 + 4$

Add $3$ and $4$ .

$x = 7$

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

$x - 4 = - 3$

Move all terms not containing $x$ to the right side of the equation.

Add $4$ to both sides of the equation.

$x = - 3 + 4$

Add $- 3$ and $4$ .

$x = 1$

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

$x = 7, 1$

x-intercept(s) in point form.

x-intercept(s): $(7, 0), (1, 0)$

Step 2

Find the y-intercepts.

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

$y = {((0) - 4)}^{2} - 9$

Solve the equation.

Remove parentheses.

$y = {(0 - 4)}^{2} - 9$

Remove parentheses.

$y = {((0) - 4)}^{2} - 9$

Simplify ${((0) - 4)}^{2} - 9$ .

Simplify each term.

Subtract $4$ from $0$ .

$y = {(- 4)}^{2} - 9$

Raise $- 4$ to the power of $2$ .

$y = 16 - 9$

Subtract $9$ from $16$ .

$y = 7$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(7, 0), (1, 0)$

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

Step 4

Find the x and y Intercepts f(x)=(x-4)^2-9

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