Find the x and y Intercepts y=(x-2)^2-1

$y = {(x - 2)}^{2} - 1$

Find the x-intercepts.

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

$0 = {(x - 2)}^{2} - 1$

Solve the equation.

Rewrite the equation as ${(x - 2)}^{2} - 1 = 0$ .

${(x - 2)}^{2} - 1 = 0$

Add $1$ to both sides of the equation.

${(x - 2)}^{2} = 1$

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

$x - 2 = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x - 2 = \pm 1$

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.

$x - 2 = 1$

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

Add $2$ to both sides of the equation.

$x = 1 + 2$

Add $1$ and $2$ .

$x = 3$

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

$x - 2 = - 1$

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

Add $2$ to both sides of the equation.

$x = - 1 + 2$

Add $- 1$ and $2$ .

$x = 1$

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

$x = 3, 1$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (1, 0)$

Find the y-intercepts.

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

$y = {((0) - 2)}^{2} - 1$

Solve the equation.

Remove parentheses.

$y = {(0 - 2)}^{2} - 1$

Remove parentheses.

$y = {((0) - 2)}^{2} - 1$

Simplify ${((0) - 2)}^{2} - 1$ .

Simplify each term.

Subtract $2$ from $0$ .

$y = {(- 2)}^{2} - 1$

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

$y = 4 - 1$

Subtract $1$ from $4$ .

$y = 3$

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

List the intersections.

x-intercept(s): $(3, 0), (1, 0)$

y-intercept(s): $(0, 3)$

Find the x and y Intercepts y=(x-2)^2-1

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