Find the x and y Intercepts y=-x^2+4x-9

$y = - x^{2} + 4 x - 9$

Find the x-intercepts.

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

$0 = - x^{2} + 4 x - 9$

Solve the equation.

Rewrite the equation as $- x^{2} + 4 x - 9 = 0$ .

$- x^{2} + 4 x - 9 = 0$

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 $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (- 1 \cdot - 9)}}{2 \cdot - 1}$

Simplify.

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 1 \cdot - 9}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{- 4 \pm \sqrt{16 + 4 \cdot - 9}}{2 \cdot - 1}$

Multiply $4$ by $- 9$ .

$x = \frac{- 4 \pm \sqrt{16 - 36}}{2 \cdot - 1}$

Subtract $36$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 20}}{2 \cdot - 1}$

Rewrite $- 20$ as $- 1 (20)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 20}}{2 \cdot - 1}$

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{20}}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{20}}{2 \cdot - 1}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (5)}}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 5}}{2 \cdot - 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{5})}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm 2 i \sqrt{5}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{- 4 \pm 2 i \sqrt{5}}{- 2}$

Simplify $\frac{- 4 \pm 2 i \sqrt{5}}{- 2}$ .

$x = 2 \pm i \sqrt{5}$

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

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 1 \cdot - 9}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{- 4 \pm \sqrt{16 + 4 \cdot - 9}}{2 \cdot - 1}$

Multiply $4$ by $- 9$ .

$x = \frac{- 4 \pm \sqrt{16 - 36}}{2 \cdot - 1}$

Subtract $36$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 20}}{2 \cdot - 1}$

Rewrite $- 20$ as $- 1 (20)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 20}}{2 \cdot - 1}$

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{20}}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{20}}{2 \cdot - 1}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (5)}}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 5}}{2 \cdot - 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{5})}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm 2 i \sqrt{5}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{- 4 \pm 2 i \sqrt{5}}{- 2}$

Simplify $\frac{- 4 \pm 2 i \sqrt{5}}{- 2}$ .

$x = 2 \pm i \sqrt{5}$

Change the $\pm$ to $+$ .

$x = 2 + i \sqrt{5}$

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

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 1 \cdot - 9}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{- 4 \pm \sqrt{16 + 4 \cdot - 9}}{2 \cdot - 1}$

Multiply $4$ by $- 9$ .

$x = \frac{- 4 \pm \sqrt{16 - 36}}{2 \cdot - 1}$

Subtract $36$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 20}}{2 \cdot - 1}$

Rewrite $- 20$ as $- 1 (20)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 20}}{2 \cdot - 1}$

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{20}}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{20}}{2 \cdot - 1}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (5)}}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 5}}{2 \cdot - 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{5})}{2 \cdot - 1}$

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

$x = \frac{- 4 \pm 2 i \sqrt{5}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{- 4 \pm 2 i \sqrt{5}}{- 2}$

Simplify $\frac{- 4 \pm 2 i \sqrt{5}}{- 2}$ .

$x = 2 \pm i \sqrt{5}$

Change the $\pm$ to $-$ .

$x = 2 - i \sqrt{5}$

The final answer is the combination of both solutions.

$x = 2 + i \sqrt{5}, 2 - i \sqrt{5}$

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 $y$ .

$y = - {(0)}^{2} + 4 (0) - 9$

Solve the equation.

Remove parentheses.

$y = - 0^{2} + 4 (0) - 9$

Remove parentheses.

$y = - {(0)}^{2} + 4 (0) - 9$

Simplify $- {(0)}^{2} + 4 (0) - 9$ .

Simplify each term.

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

$y = - 0 + 4 (0) - 9$

Multiply $- 1$ by $0$ .

$y = 0 + 4 (0) - 9$

Multiply $4$ by $0$ .

$y = 0 + 0 - 9$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 9$

Subtract $9$ from $0$ .

$y = - 9$

y-intercept(s) in point form.

y-intercept(s): $(0, - 9)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - 9)$

Find the x and y Intercepts y=-x^2+4x-9

Related Questions

Support LCMGCF.com by disabling your adblocker.