Find the x and y Intercepts x^2+y^2+4x-4y-17=0

$x^{2} + y^{2} + 4 x - 4 y - 17 = 0$

Step 1

Find the x-intercepts.

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

$x^{2} + {(0)}^{2} + 4 x - 4 \cdot 0 - 17 = 0$

Solve the equation.

Simplify $x^{2} + {(0)}^{2} + 4 x - 4 \cdot 0 - 17$ .

Simplify each term.

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

$x^{2} + 0 + 4 x - 4 \cdot 0 - 17 = 0$

Multiply $- 4$ by $0$ .

$x^{2} + 0 + 4 x + 0 - 17 = 0$

Combine the opposite terms in $x^{2} + 0 + 4 x + 0 - 17$ .

Add $x^{2}$ and $0$ .

$x^{2} + 4 x + 0 - 17 = 0$

Add $x^{2} + 4 x$ and $0$ .

$x^{2} + 4 x - 17 = 0$

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 $c = - 17$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (1 \cdot - 17)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 17$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$x = \frac{- 4 \pm \sqrt{16 + 68}}{2 \cdot 1}$

Add $16$ and $68$ .

$x = \frac{- 4 \pm \sqrt{84}}{2 \cdot 1}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$x = \frac{- 4 \pm \sqrt{4 (21)}}{2 \cdot 1}$

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

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 2 \sqrt{21}}{2}$

Simplify $\frac{- 4 \pm 2 \sqrt{21}}{2}$ .

$x = - 2 \pm \sqrt{21}$

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

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 17$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$x = \frac{- 4 \pm \sqrt{16 + 68}}{2 \cdot 1}$

Add $16$ and $68$ .

$x = \frac{- 4 \pm \sqrt{84}}{2 \cdot 1}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$x = \frac{- 4 \pm \sqrt{4 (21)}}{2 \cdot 1}$

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

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 2 \sqrt{21}}{2}$

Simplify $\frac{- 4 \pm 2 \sqrt{21}}{2}$ .

$x = - 2 \pm \sqrt{21}$

Change the $\pm$ to $+$ .

$x = - 2 + \sqrt{21}$

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

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 17$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$x = \frac{- 4 \pm \sqrt{16 + 68}}{2 \cdot 1}$

Add $16$ and $68$ .

$x = \frac{- 4 \pm \sqrt{84}}{2 \cdot 1}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$x = \frac{- 4 \pm \sqrt{4 (21)}}{2 \cdot 1}$

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

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 2 \sqrt{21}}{2}$

Simplify $\frac{- 4 \pm 2 \sqrt{21}}{2}$ .

$x = - 2 \pm \sqrt{21}$

Change the $\pm$ to $-$ .

$x = - 2 - \sqrt{21}$

The final answer is the combination of both solutions.

$x = - 2 + \sqrt{21}, - 2 - \sqrt{21}$

x-intercept(s) in point form.

x-intercept(s): $(- 2 + \sqrt{21}, 0), (- 2 - \sqrt{21}, 0)$

Step 2

Find the y-intercepts.

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

${(0)}^{2} + y^{2} + 4 (0) - 4 y - 17 = 0$

Solve the equation.

Simplify ${(0)}^{2} + y^{2} + 4 (0) - 4 y - 17$ .

Simplify each term.

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

$0 + y^{2} + 4 (0) - 4 y - 17 = 0$

Multiply $4$ by $0$ .

$0 + y^{2} + 0 - 4 y - 17 = 0$

Combine the opposite terms in $0 + y^{2} + 0 - 4 y - 17$ .

Add $0$ and $y^{2}$ .

$y^{2} + 0 - 4 y - 17 = 0$

Add $y^{2}$ and $0$ .

$y^{2} - 4 y - 17 = 0$

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 $c = - 17$ into the quadratic formula and solve for $y$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (1 \cdot - 17)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

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

$y = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 17$ .

Multiply $- 4$ by $1$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$y = \frac{4 \pm \sqrt{16 + 68}}{2 \cdot 1}$

Add $16$ and $68$ .

$y = \frac{4 \pm \sqrt{84}}{2 \cdot 1}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$y = \frac{4 \pm \sqrt{4 (21)}}{2 \cdot 1}$

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

$y = \frac{4 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{4 \pm 2 \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{4 \pm 2 \sqrt{21}}{2}$

Simplify $\frac{4 \pm 2 \sqrt{21}}{2}$ .

$y = 2 \pm \sqrt{21}$

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

Simplify the numerator.

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

$y = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 17$ .

Multiply $- 4$ by $1$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$y = \frac{4 \pm \sqrt{16 + 68}}{2 \cdot 1}$

Add $16$ and $68$ .

$y = \frac{4 \pm \sqrt{84}}{2 \cdot 1}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$y = \frac{4 \pm \sqrt{4 (21)}}{2 \cdot 1}$

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

$y = \frac{4 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{4 \pm 2 \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{4 \pm 2 \sqrt{21}}{2}$

Simplify $\frac{4 \pm 2 \sqrt{21}}{2}$ .

$y = 2 \pm \sqrt{21}$

Change the $\pm$ to $+$ .

$y = 2 + \sqrt{21}$

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

Simplify the numerator.

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

$y = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 17$ .

Multiply $- 4$ by $1$ .

$y = \frac{4 \pm \sqrt{16 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$y = \frac{4 \pm \sqrt{16 + 68}}{2 \cdot 1}$

Add $16$ and $68$ .

$y = \frac{4 \pm \sqrt{84}}{2 \cdot 1}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$y = \frac{4 \pm \sqrt{4 (21)}}{2 \cdot 1}$

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

$y = \frac{4 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{4 \pm 2 \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{4 \pm 2 \sqrt{21}}{2}$

Simplify $\frac{4 \pm 2 \sqrt{21}}{2}$ .

$y = 2 \pm \sqrt{21}$

Change the $\pm$ to $-$ .

$y = 2 - \sqrt{21}$

The final answer is the combination of both solutions.

$y = 2 + \sqrt{21}, 2 - \sqrt{21}$

y-intercept(s) in point form.

y-intercept(s): $(0, 2 + \sqrt{21}), (0, 2 - \sqrt{21})$

Step 3

List the intersections.

x-intercept(s): $(- 2 + \sqrt{21}, 0), (- 2 - \sqrt{21}, 0)$

y-intercept(s): $(0, 2 + \sqrt{21}), (0, 2 - \sqrt{21})$

Step 4

Find the x and y Intercepts x^2+y^2+4x-4y-17=0

Related Questions

Support LCMGCF.com by disabling your adblocker.