To find \( f(-7) \) for the function \( f(x) = 2x^2 - 1 \), we substitute \( x = -7 \) into the equation and solve:

\[
f(-7) = 2(-7)^2 - 1
\]

First, calculate \( (-7)^2 \):

\[
(-7)^2 = 49
\]

Then, multiply by 2:

\[
2 \times 49 = 98
\]

Finally, subtract 1:

\[
98 - 1 = 97
\]

So, \( f(-7) = 97 \).

Would you like any further details or have other questions?

Here are 5 related questions to explore:
1. What is the value of \( f(0) \) for the function \( f(x) = 2x^2 - 1 \)?
2. How does the function \( f(x) = 2x^2 - 1 \) behave as \( x \) approaches infinity?
3. What are the intercepts of the function \( f(x) = 2x^2 - 1 \)?
4. How do you determine whether the function \( f(x) = 2x^2 - 1 \) is increasing or decreasing at a specific point?
5. How would the function change if the equation were \( f(x) = -2x^2 - 1 \)?

**Tip:** When substituting negative values, remember that squaring a negative number results in a positive value.

Learn how to calculate f(-7) for the function f(x) = 2x^2 - 1 using substitution and basic algebraic operations. This problem explores quadratic equations and their application in function evaluation. Suitable for high school students and those interested in algebraic functions.

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