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

The equation provided is:

\[
y = 6x^2 - 6
\]

To find the intercepts, we need to calculate both the **y-intercept** and the **x-intercepts**.

### 1. **Y-intercept**:
The y-intercept occurs where \( x = 0 \). Substitute \( x = 0 \) into the equation:

\[
y = 6(0)^2 - 6 = -6
\]

Thus, the y-intercept is at \( (0, -6) \).

### 2. **X-intercepts**:
The x-intercepts occur where \( y = 0 \). Set \( y = 0 \) in the equation and solve for \( x \):

\[
0 = 6x^2 - 6
\]
\[
6x^2 = 6
\]
\[
x^2 = 1
\]
\[
x = \pm 1
\]

Thus, the x-intercepts are at \( (1, 0) \) and \( (-1, 0) \).

### Summary of intercepts:
- Y-intercept: \( (0, -6) \)
- X-intercepts: \( (1, 0) \) and \( (-1, 0) \)

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the vertex of the parabola \( y = 6x^2 - 6 \)?
2. How would you find the axis of symmetry for this equation?
3. What is the effect of changing the coefficient of \( x^2 \) on the graph?
4. How does the graph of \( y = 6x^2 - 6 \) compare to \( y = x^2 \)?
5. Can you solve similar equations where the constant is positive?

**Tip:** The y-intercept of any quadratic equation can be quickly found by evaluating it at \( x = 0 \).

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

Learn how to find the x and y intercepts of the quadratic equation y = 6x^2 - 6 with a step-by-step solution. This problem involves calculating the intercepts of a parabola, suitable for students in Grades 8-10. Key topics include quadratic functions, the zero-product property, and symmetry.

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