Find the x and y Intercepts 4x^2+9y=36

$4 x^{2} + 9 y = 36$

Find the x-intercepts.

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

$4 x^{2} + 9 (0) = 36$

Solve the equation.

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

Multiply $9$ by $0$ .

$4 x^{2} + 0 = 36$

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

$4 x^{2} = 36$

Divide each term in $4 x^{2} = 36$ by $4$ and simplify.

Divide each term in $4 x^{2} = 36$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{36}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{36}{4}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{36}{4}$

Simplify the right side.

Divide $36$ by $4$ .

$x^{2} = 9$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

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

$x = \pm 3$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 3, 0)$

Find the y-intercepts.

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

$4 {(0)}^{2} + 9 y = 36$

Solve the equation.

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

Simplify each term.

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

$4 \cdot 0 + 9 y = 36$

Multiply $4$ by $0$ .

$0 + 9 y = 36$

Add $0$ and $9 y$ .

$9 y = 36$

Divide each term in $9 y = 36$ by $9$ and simplify.

Divide each term in $9 y = 36$ by $9$ .

$\frac{9 y}{9} = \frac{36}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{36}{9}$

Divide $y$ by $1$ .

$y = \frac{36}{9}$

Simplify the right side.

Divide $36$ by $9$ .

$y = 4$

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

List the intersections.

x-intercept(s): $(3, 0), (- 3, 0)$

y-intercept(s): $(0, 4)$

Find the x and y Intercepts 4x^2+9y=36

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