Math Problem Statement

Use the graph of f to determine each indicated function value.

Solution

Let's analyze the graph to solve the problems.

The graph provided is a parabolic curve, and based on the labeled points, it seems like the function is quadratic. The points marked are:

  • (6,5)(-6, 5)
  • (4,0)(-4, 0)
  • (0,4)(0, -4)
  • (4,0)(4, 0)
  • (6,5)(6, 5)

Now, let's address each function value requested:

20. f(6)f(-6)

From the graph, f(6)=5f(-6) = 5 (since the point (6,5)(-6, 5) is on the graph).

21. f(4)f(-4)

From the graph, f(4)=0f(-4) = 0 (since the point (4,0)(-4, 0) is on the graph).

22. f(0)f(0)

From the graph, f(0)=4f(0) = -4 (since the point (0,4)(0, -4) is on the graph).

23. f(4)f(4)

From the graph, f(4)=0f(4) = 0 (since the point (4,0)(4, 0) is on the graph).

24. f(6)f(6)

From the graph, f(6)=5f(6) = 5 (since the point (6,5)(6, 5) is on the graph).


Would you like further details or explanations for any of these answers?

Here are five related questions to deepen your understanding:

  1. How can you determine if a function is even or odd using its graph?
  2. What are the key features of quadratic functions in general?
  3. How can the vertex of a parabola be identified on a graph?
  4. How do you find the axis of symmetry of a parabola?
  5. Can you derive the equation of the parabola based on the given points?

Tip: The vertex form of a quadratic equation is f(x)=a(xh)2+kf(x) = a(x-h)^2 + k, where (h,k)(h, k) is the vertex. Try using this to derive the equation of the given function!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Graph Interpretation

Formulas

f(x) = ax^2 + bx + c (Quadratic function)
Vertex form: f(x) = a(x-h)^2 + k

Theorems

Quadratic Function Properties
Symmetry in Parabolas

Suitable Grade Level

Grades 8-10