Find the​ intercept(s) of the following equation.
y equals 6 x squared minus 6

To find the intercepts of the equation \( y = 6x^2 - 6 \), we need to determine both the **y-intercept** and the **x-intercepts**.

### 1. **Finding the y-intercept:**

The y-intercept occurs when \( x = 0 \). So, substitute \( x = 0 \) into the equation:
\[
y = 6(0)^2 - 6 = -6
\]
Thus, the **y-intercept** is at \( (0, -6) \).

### 2. **Finding the x-intercepts:**

The x-intercepts occur when \( y = 0 \). Set the equation equal to 0 and solve for \( x \):
\[
0 = 6x^2 - 6
\]
Add 6 to both sides:
\[
6 = 6x^2
\]
Now, divide both sides by 6:
\[
x^2 = 1
\]
Take the square root of both sides:
\[
x = \pm 1
\]
So, the **x-intercepts** are \( (1, 0) \) and \( (-1, 0) \).

### Conclusion:
- **y-intercept**: \( (0, -6) \)
- **x-intercepts**: \( (1, 0) \) and \( (-1, 0) \)

Would you like further clarification on any of these steps?

Here are 5 related questions:
1. How do you find intercepts for more complex polynomial equations?
2. What is the general process for solving quadratic equations?
3. Can a parabola have more than two x-intercepts?
4. What does the symmetry of the parabola suggest about its intercepts?
5. How can you determine the vertex of a quadratic equation?

**Tip:** For quadratic equations, the discriminant \( b^2 - 4ac \) helps determine the nature of the x-intercepts (real or imaginary).

Find the intercept(s) of the following equation. y equals 6 x squared minus 6

Learn how to find the intercepts of the quadratic equation y = 6x^2 - 6. This step-by-step solution covers finding both the x-intercepts and y-intercepts using key algebraic concepts like the quadratic formula. Suitable for students in Grades 8-10.

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