https://file.aiquickdraw.com/mathbot/file/1726386565694t72lt4no.jpg

https://file.aiquickdraw.com/mathbot/file/1726386654171c0nt1dp2.jpg

The two equations in the images you've provided are:

1. First equation:
   \[
   f(0) = -(0)^2 - 1
   \]
   Simplifying this:
   \[
   f(0) = -0 - 1 = -1
   \]

2. Second equation:
   \[
   f(x) = -(x)^2 + 1
   \]
   This represents a quadratic function:
   \[
   f(x) = -x^2 + 1
   \]
   which is a downward-facing parabola with its vertex at \( (0, 1) \).

Let me know if you need more details or have any further questions.

Here are some related questions to consider:
1. What is the domain and range of the function \( f(x) = -x^2 + 1 \)?
2. What are the x-intercepts and y-intercepts of \( f(x) = -x^2 + 1 \)?
3. How does the graph of \( f(x) = -x^2 + 1 \) compare to \( f(x) = x^2 \)?
4. What is the vertex of the parabola \( f(x) = -x^2 + 1 \)?
5. How would you solve for \( f(x) = 0 \)?

**Tip**: When working with parabolas, the sign of the coefficient of \( x^2 \) determines whether the parabola opens upwards (positive) or downwards (negative).

Evaluate the given functions at specified points.

Discover how to evaluate quadratic functions at specific points using algebraic methods. This guide covers the properties of quadratic functions, including their vertex and axis of symmetry, and demonstrates function evaluation with examples. Suitable for students in Grades 8-10.

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