Find the x and y Intercepts y=x^2-4x+8

$y = x^{2} - 4 x + 8$

Step 1

Find the x-intercepts.

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

$0 = x^{2} - 4 x + 8$

Solve the equation.

Rewrite the equation as $x^{2} - 4 x + 8 = 0$ .

$x^{2} - 4 x + 8 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = - 4$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (1 \cdot 8)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

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

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 8$ .

Multiply $- 4$ by $1$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 8}}{2 \cdot 1}$

Multiply $- 4$ by $8$ .

$x = \frac{4 \pm \sqrt{16 - 32}}{2 \cdot 1}$

Subtract $32$ from $16$ .

$x = \frac{4 \pm \sqrt{- 16}}{2 \cdot 1}$

Rewrite $- 16$ as $- 1 (16)$ .

$x = \frac{4 \pm \sqrt{- 1 \cdot 16}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$x = \frac{4 \pm \sqrt{- 1} \cdot \sqrt{16}}{2 \cdot 1}$

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

$x = \frac{4 \pm i \cdot \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

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

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

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

Move $4$ to the left of $i$ .

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

Multiply $2$ by $1$ .

$x = \frac{4 \pm 4 i}{2}$

Simplify $\frac{4 \pm 4 i}{2}$ .

$x = 2 \pm 2 i$

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

Simplify the numerator.

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

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 8$ .

Multiply $- 4$ by $1$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 8}}{2 \cdot 1}$

Multiply $- 4$ by $8$ .

$x = \frac{4 \pm \sqrt{16 - 32}}{2 \cdot 1}$

Subtract $32$ from $16$ .

$x = \frac{4 \pm \sqrt{- 16}}{2 \cdot 1}$

Rewrite $- 16$ as $- 1 (16)$ .

$x = \frac{4 \pm \sqrt{- 1 \cdot 16}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$x = \frac{4 \pm \sqrt{- 1} \cdot \sqrt{16}}{2 \cdot 1}$

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

$x = \frac{4 \pm i \cdot \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

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

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

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

Move $4$ to the left of $i$ .

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

Multiply $2$ by $1$ .

$x = \frac{4 \pm 4 i}{2}$

Simplify $\frac{4 \pm 4 i}{2}$ .

$x = 2 \pm 2 i$

Change the $\pm$ to $+$ .

$x = 2 + 2 i$

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

Simplify the numerator.

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

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 8$ .

Multiply $- 4$ by $1$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 8}}{2 \cdot 1}$

Multiply $- 4$ by $8$ .

$x = \frac{4 \pm \sqrt{16 - 32}}{2 \cdot 1}$

Subtract $32$ from $16$ .

$x = \frac{4 \pm \sqrt{- 16}}{2 \cdot 1}$

Rewrite $- 16$ as $- 1 (16)$ .

$x = \frac{4 \pm \sqrt{- 1 \cdot 16}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$x = \frac{4 \pm \sqrt{- 1} \cdot \sqrt{16}}{2 \cdot 1}$

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

$x = \frac{4 \pm i \cdot \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

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

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

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

Move $4$ to the left of $i$ .

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

Multiply $2$ by $1$ .

$x = \frac{4 \pm 4 i}{2}$

Simplify $\frac{4 \pm 4 i}{2}$ .

$x = 2 \pm 2 i$

Change the $\pm$ to $-$ .

$x = 2 - 2 i$

The final answer is the combination of both solutions.

$x = 2 + 2 i, 2 - 2 i$

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

$y = {(0)}^{2} - 4 \cdot 0 + 8$

Solve the equation.

Remove parentheses.

$y = 0^{2} - 4 \cdot 0 + 8$

Remove parentheses.

$y = {(0)}^{2} - 4 \cdot 0 + 8$

Simplify ${(0)}^{2} - 4 \cdot 0 + 8$ .

Simplify each term.

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

$y = 0 - 4 \cdot 0 + 8$

Multiply $- 4$ by $0$ .

$y = 0 + 0 + 8$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 8$

Add $0$ and $8$ .

$y = 8$

y-intercept(s) in point form.

y-intercept(s): $(0, 8)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 8)$

Step 4

Find the x and y Intercepts y=x^2-4x+8

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