To solve the equation \( f(t) = 6 \) where \( f(t) = t^2 - 64 \), we need to find the value(s) of \( t \) that satisfy this equation.

Given:
\[
f(t) = t^2 - 64
\]
Set \( f(t) = 6 \):
\[
t^2 - 64 = 6
\]
To solve for \( t \), follow these steps:

1. **Add 64 to both sides**:
   \[
   t^2 = 6 + 64
   \]
   \[
   t^2 = 70
   \]

2. **Take the square root of both sides**:
   \[
   t = \pm\sqrt{70}
   \]

So, the solutions are:
\[
t = \sqrt{70} \quad \text{or} \quad t = -\sqrt{70}
\]

**Exact solutions**: \( t = \pm\sqrt{70} \).

Would you like more details or have any questions?

Here are five related questions:

1. How do you approximate \( \sqrt{70} \) to two decimal places?
2. What are the intercepts of the function \( f(t) = t^2 - 64 \) with the horizontal line \( y = 6 \)?
3. How would you solve the equation \( f(t) = -6 \)?
4. What is the significance of the discriminant in quadratic equations?
5. How can you graph the function \( f(t) = t^2 - 64 \) and the line \( y = 6 \)?

**Tip:** When solving quadratic equations, always check if the solution involves taking the square root, as it can lead to both positive and negative roots.

Learn how to solve the quadratic equation f(t) = 6 where f(t) = t^2 - 64. Detailed step-by-step solution provided, covering quadratic equations and square roots. Suitable for students in Grades 9-12.

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