Find the x and y Intercepts y=x^2-6x+10

$y = x^{2} - 6 x + 10$

Find the x-intercepts.

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

$0 = x^{2} - 6 x + 10$

Solve the equation.

Rewrite the equation as $x^{2} - 6 x + 10 = 0$ .

$x^{2} - 6 x + 10 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = - 6$ , and $c = 10$ into the quadratic formula and solve for $x$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot 10)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $10$ .

$x = \frac{6 \pm \sqrt{36 - 40}}{2 \cdot 1}$

Subtract $40$ from $36$ .

$x = \frac{6 \pm \sqrt{- 4}}{2 \cdot 1}$

Rewrite $- 4$ as $- 1 (4)$ .

$x = \frac{6 \pm \sqrt{- 1 \cdot 4}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$x = \frac{6 \pm \sqrt{- 1} \cdot \sqrt{4}}{2 \cdot 1}$

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

$x = \frac{6 \pm i \cdot \sqrt{4}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{6 \pm i \cdot \sqrt{2^{2}}}{2 \cdot 1}$

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

$x = \frac{6 \pm i \cdot 2}{2 \cdot 1}$

Move $2$ to the left of $i$ .

$x = \frac{6 \pm 2 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{6 \pm 2 i}{2}$

Simplify $\frac{6 \pm 2 i}{2}$ .

$x = 3 \pm i$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $10$ .

$x = \frac{6 \pm \sqrt{36 - 40}}{2 \cdot 1}$

Subtract $40$ from $36$ .

$x = \frac{6 \pm \sqrt{- 4}}{2 \cdot 1}$

Rewrite $- 4$ as $- 1 (4)$ .

$x = \frac{6 \pm \sqrt{- 1 \cdot 4}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$x = \frac{6 \pm \sqrt{- 1} \cdot \sqrt{4}}{2 \cdot 1}$

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

$x = \frac{6 \pm i \cdot \sqrt{4}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{6 \pm i \cdot \sqrt{2^{2}}}{2 \cdot 1}$

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

$x = \frac{6 \pm i \cdot 2}{2 \cdot 1}$

Move $2$ to the left of $i$ .

$x = \frac{6 \pm 2 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{6 \pm 2 i}{2}$

Simplify $\frac{6 \pm 2 i}{2}$ .

$x = 3 \pm i$

Change the $\pm$ to $+$ .

$x = 3 + i$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $10$ .

$x = \frac{6 \pm \sqrt{36 - 40}}{2 \cdot 1}$

Subtract $40$ from $36$ .

$x = \frac{6 \pm \sqrt{- 4}}{2 \cdot 1}$

Rewrite $- 4$ as $- 1 (4)$ .

$x = \frac{6 \pm \sqrt{- 1 \cdot 4}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$x = \frac{6 \pm \sqrt{- 1} \cdot \sqrt{4}}{2 \cdot 1}$

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

$x = \frac{6 \pm i \cdot \sqrt{4}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{6 \pm i \cdot \sqrt{2^{2}}}{2 \cdot 1}$

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

$x = \frac{6 \pm i \cdot 2}{2 \cdot 1}$

Move $2$ to the left of $i$ .

$x = \frac{6 \pm 2 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{6 \pm 2 i}{2}$

Simplify $\frac{6 \pm 2 i}{2}$ .

$x = 3 \pm i$

Change the $\pm$ to $-$ .

$x = 3 - i$

The final answer is the combination of both solutions.

$x = 3 + i, 3 - i$

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = {(0)}^{2} - 6 \cdot 0 + 10$

Solve the equation.

Remove parentheses.

$y = 0^{2} - 6 \cdot 0 + 10$

Remove parentheses.

$y = {(0)}^{2} - 6 \cdot 0 + 10$

Simplify ${(0)}^{2} - 6 \cdot 0 + 10$ .

Simplify each term.

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

$y = 0 - 6 \cdot 0 + 10$

Multiply $- 6$ by $0$ .

$y = 0 + 0 + 10$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 10$

Add $0$ and $10$ .

$y = 10$

y-intercept(s) in point form.

y-intercept(s): $(0, 10)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 10)$

Find the x and y Intercepts y=x^2-6x+10

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