Find the x and y Intercepts x^2+y^2+4x-6y+4=0

$x^{2} + y^{2} + 4 x - 6 y + 4 = 0$

Find the x-intercepts.

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

$x^{2} + {(0)}^{2} + 4 x - 6 \cdot 0 + 4 = 0$

Solve the equation.

Simplify $x^{2} + {(0)}^{2} + 4 x - 6 \cdot 0 + 4$ .

Simplify each term.

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

$x^{2} + 0 + 4 x - 6 \cdot 0 + 4 = 0$

Multiply $- 6$ by $0$ .

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

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

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

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

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

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

Factor using the perfect square rule.

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

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

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot x \cdot 2$

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot 2 + 2^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 2$ .

${(x + 2)}^{2} = 0$

Set the $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

x-intercept(s) in point form.

x-intercept(s): $(- 2, 0)$

Find the y-intercepts.

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

${(0)}^{2} + y^{2} + 4 (0) - 6 y + 4 = 0$

Solve the equation.

Simplify ${(0)}^{2} + y^{2} + 4 (0) - 6 y + 4$ .

Simplify each term.

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

$0 + y^{2} + 4 (0) - 6 y + 4 = 0$

Multiply $4$ by $0$ .

$0 + y^{2} + 0 - 6 y + 4 = 0$

Combine the opposite terms in $0 + y^{2} + 0 - 6 y + 4$ .

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

$y^{2} + 0 - 6 y + 4 = 0$

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

$y^{2} - 6 y + 4 = 0$

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 $c = 4$ into the quadratic formula and solve for $y$ .

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

Simplify.

Simplify the numerator.

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $4$ .

$y = \frac{6 \pm \sqrt{36 - 16}}{2 \cdot 1}$

Subtract $16$ from $36$ .

$y = \frac{6 \pm \sqrt{20}}{2 \cdot 1}$

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

Factor $4$ out of $20$ .

$y = \frac{6 \pm \sqrt{4 (5)}}{2 \cdot 1}$

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

$y = \frac{6 \pm \sqrt{2^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{6 \pm 2 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{6 \pm 2 \sqrt{5}}{2}$

Simplify $\frac{6 \pm 2 \sqrt{5}}{2}$ .

$y = 3 \pm \sqrt{5}$

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

Simplify the numerator.

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $4$ .

$y = \frac{6 \pm \sqrt{36 - 16}}{2 \cdot 1}$

Subtract $16$ from $36$ .

$y = \frac{6 \pm \sqrt{20}}{2 \cdot 1}$

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

Factor $4$ out of $20$ .

$y = \frac{6 \pm \sqrt{4 (5)}}{2 \cdot 1}$

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

$y = \frac{6 \pm \sqrt{2^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{6 \pm 2 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{6 \pm 2 \sqrt{5}}{2}$

Simplify $\frac{6 \pm 2 \sqrt{5}}{2}$ .

$y = 3 \pm \sqrt{5}$

Change the $\pm$ to $+$ .

$y = 3 + \sqrt{5}$

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

Simplify the numerator.

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $4$ .

$y = \frac{6 \pm \sqrt{36 - 16}}{2 \cdot 1}$

Subtract $16$ from $36$ .

$y = \frac{6 \pm \sqrt{20}}{2 \cdot 1}$

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

Factor $4$ out of $20$ .

$y = \frac{6 \pm \sqrt{4 (5)}}{2 \cdot 1}$

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

$y = \frac{6 \pm \sqrt{2^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{6 \pm 2 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{6 \pm 2 \sqrt{5}}{2}$

Simplify $\frac{6 \pm 2 \sqrt{5}}{2}$ .

$y = 3 \pm \sqrt{5}$

Change the $\pm$ to $-$ .

$y = 3 - \sqrt{5}$

The final answer is the combination of both solutions.

$y = 3 + \sqrt{5}, 3 - \sqrt{5}$

y-intercept(s) in point form.

y-intercept(s): $(0, 3 + \sqrt{5}), (0, 3 - \sqrt{5})$

List the intersections.

x-intercept(s): $(- 2, 0)$

y-intercept(s): $(0, 3 + \sqrt{5}), (0, 3 - \sqrt{5})$

Find the x and y Intercepts x^2+y^2+4x-6y+4=0

Related Questions

Support LCMGCF.com by disabling your adblocker.