Find the x and y Intercepts y=6x^2-6

$y = 6 x^{2} - 6$

Step 1

Find the x-intercepts.

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

$0 = 6 x^{2} - 6$

Solve the equation.

Rewrite the equation as $6 x^{2} - 6 = 0$ .

$6 x^{2} - 6 = 0$

Add $6$ to both sides of the equation.

$6 x^{2} = 6$

Divide each term in $6 x^{2} = 6$ by $6$ and simplify.

Divide each term in $6 x^{2} = 6$ by $6$ .

$\frac{6 x^{2}}{6} = \frac{6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x^{2}}{6} = \frac{6}{6}$

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

$x^{2} = \frac{6}{6}$

Simplify the right side.

Divide $6$ by $6$ .

$x^{2} = 1$

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

$x = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x = \pm 1$

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.

$x = 1$

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

$x = - 1$

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

$x = 1, - 1$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 1, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

$y = 6 \cdot 0^{2} - 6$

Remove parentheses.

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

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

Simplify each term.

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

$y = 6 \cdot 0 - 6$

Multiply $6$ by $0$ .

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

y-intercept(s) in point form.

y-intercept(s): $(0, - 6)$

Step 3

List the intersections.

x-intercept(s): $(1, 0), (- 1, 0)$

y-intercept(s): $(0, - 6)$

Step 4

Find the x and y Intercepts y=6x^2-6

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