Find the x and y Intercepts a(x)=(x-3)^2-2

$a (x) = {(x - 3)}^{2} - 2$

Step 1

Find the x-intercepts.

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

$0 = {(x - 3)}^{2} - 2$

Solve the equation.

Rewrite the equation as ${(x - 3)}^{2} - 2 = 0$ .

${(x - 3)}^{2} - 2 = 0$

Add $2$ to both sides of the equation.

${(x - 3)}^{2} = 2$

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

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

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.

$x - 3 = \sqrt{2}$

Add $3$ to both sides of the equation.

$x = \sqrt{2} + 3$

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

$x - 3 = - \sqrt{2}$

Add $3$ to both sides of the equation.

$x = - \sqrt{2} + 3$

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

$x = \sqrt{2} + 3, - \sqrt{2} + 3$

x-intercept(s) in point form.

x-intercept(s): $(\sqrt{2} + 3, 0), (- \sqrt{2} + 3, 0)$

Step 2

Find the y-intercepts.

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

$y = {((0) - 3)}^{2} - 2$

Solve the equation.

Remove parentheses.

$y = {(0 - 3)}^{2} - 2$

Remove parentheses.

$y = {((0) - 3)}^{2} - 2$

Simplify ${((0) - 3)}^{2} - 2$ .

Simplify each term.

Subtract $3$ from $0$ .

$y = {(- 3)}^{2} - 2$

Raise $- 3$ to the power of $2$ .

$y = 9 - 2$

Subtract $2$ from $9$ .

$y = 7$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\sqrt{2} + 3, 0), (- \sqrt{2} + 3, 0)$

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

Step 4

Find the x and y Intercepts a(x)=(x-3)^2-2

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