Concept Check Match each function with its graph without...

Concept Check Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window:
(GRAPHS CANNOT COPY)
$$f(x)=-(x-4)^{2}+3$$

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Key Concepts

Graphing Quadratic Functions

Graphing quadratic functions involves plotting the parabola by using information like the vertex, axis of symmetry, and the direction in which it opens. By analyzing the function's equation, especially when written in vertex form, one can sketch an accurate graph without needing a calculator.

Reflection

Reflection is the transformation that flips the graph over a particular axis. In quadratic functions, a negative 'a' value in the vertex form causes the parabola to open downwards, effectively reflecting it vertically relative to the horizontal line through the vertex.

Vertex Form of Quadratic Functions

Quadratic functions can be expressed in vertex form as f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola. This form makes it clear how the function is shifted relative to the basic quadratic y = x², and it simplifies the process of identifying the vertex and other key features of the graph.

Transformation of Functions

This concept involves altering the basic graph of a function by translating, stretching, compressing, or reflecting it. These operations change the position or shape of the graph without altering its overall form, helping to visualize how modifications in the function's equation affect the graph.