Find the x and y Intercepts (x-1)^2+6

${(x - 1)}^{2} + 6$

Step 1

Write ${(x - 1)}^{2} + 6$ as an equation.

$y = {(x - 1)}^{2} + 6$

Step 2

Find the x-intercepts.

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

$0 = {(x - 1)}^{2} + 6$

Solve the equation.

Rewrite the equation as ${(x - 1)}^{2} + 6 = 0$ .

${(x - 1)}^{2} + 6 = 0$

Subtract $6$ from both sides of the equation.

${(x - 1)}^{2} = - 6$

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

$x - 1 = \pm \sqrt{- 6}$

Simplify $\pm \sqrt{- 6}$ .

Rewrite $- 6$ as $- 1 (6)$ .

$x - 1 = \pm \sqrt{- 1 (6)}$

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$x - 1 = \pm \sqrt{- 1} \cdot \sqrt{6}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x - 1 = \pm i \sqrt{6}$

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.

$x - 1 = i \sqrt{6}$

Add $1$ to both sides of the equation.

$x = i \sqrt{6} + 1$

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

$x - 1 = - i \sqrt{6}$

Add $1$ to both sides of the equation.

$x = - i \sqrt{6} + 1$

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

$x = i \sqrt{6} + 1, - i \sqrt{6} + 1$

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

x-intercept(s): $None$

Step 3

Find the y-intercepts.

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

$y = {((0) - 1)}^{2} + 6$

Solve the equation.

Remove parentheses.

$y = {(0 - 1)}^{2} + 6$

Remove parentheses.

$y = {((0) - 1)}^{2} + 6$

Simplify ${((0) - 1)}^{2} + 6$ .

Simplify each term.

Subtract $1$ from $0$ .

$y = {(- 1)}^{2} + 6$

Raise $- 1$ to the power of $2$ .

$y = 1 + 6$

Add $1$ and $6$ .

$y = 7$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $None$

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

Step 5

Find the x and y Intercepts (x-1)^2+6

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