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 $x = 0$.