Find the x and y Intercepts f(x)=3x^2-36

$f (x) = 3 x^{2} - 36$

Step 1

Find the x-intercepts.

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

$0 = 3 x^{2} - 36$

Solve the equation.

Rewrite the equation as $3 x^{2} - 36 = 0$ .

$3 x^{2} - 36 = 0$

Add $36$ to both sides of the equation.

$3 x^{2} = 36$

Divide each term in $3 x^{2} = 36$ by $3$ and simplify.

Divide each term in $3 x^{2} = 36$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{36}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{36}{3}$

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

$x^{2} = \frac{36}{3}$

Simplify the right side.

Divide $36$ by $3$ .

$x^{2} = 12$

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

$x = \pm \sqrt{12}$

Simplify $\pm \sqrt{12}$ .

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$x = \pm \sqrt{4 (3)}$

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

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

Pull terms out from under the radical.

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

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.

$x = 2 \sqrt{3}$

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

$x = - 2 \sqrt{3}$

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

$x = 2 \sqrt{3}, - 2 \sqrt{3}$

x-intercept(s) in point form.

x-intercept(s): $(2 \sqrt{3}, 0), (- 2 \sqrt{3}, 0)$

Step 2

Find the y-intercepts.

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

$y = 3 {(0)}^{2} - 36$

Solve the equation.

Remove parentheses.

$y = 3 \cdot 0^{2} - 36$

Remove parentheses.

$y = 3 {(0)}^{2} - 36$

Simplify $3 {(0)}^{2} - 36$ .

Simplify each term.

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

$y = 3 \cdot 0 - 36$

Multiply $3$ by $0$ .

$y = 0 - 36$

Subtract $36$ from $0$ .

$y = - 36$

y-intercept(s) in point form.

y-intercept(s): $(0, - 36)$

Step 3

List the intersections.

x-intercept(s): $(2 \sqrt{3}, 0), (- 2 \sqrt{3}, 0)$

y-intercept(s): $(0, - 36)$

Step 4

Find the x and y Intercepts f(x)=3x^2-36

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