Matching In Exercises 7-12, match the quadratic function with its graph. [The graphs are labeled

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Matching In Exercises 7-12, match the quadratic function...

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Key Concepts

Graph Transformations

Graph transformations explain how a basic function is shifted, stretched, reflected, or compressed to produce a new graph. In the vertex form, the (h, k) in (x - h)^2 + k represent horizontal and vertical translations respectively, while the coefficient a indicates vertical scaling and determines whether the parabola opens upward or downward.

Vertex Form of a Quadratic

Writing a quadratic function in vertex form, f(x) = a(x - h)^2 + k, makes it easy to identify the vertex (h, k) of the parabola. This form highlights the function’s key features, including the vertex’s coordinates and the effect of the coefficient a on the width and direction (opening upward or downward) of the parabola.

Quadratic Function

Quadratic functions are second-degree polynomial functions that produce parabolic graphs. They are characterized by a squared term and have properties such as a vertex, an axis of symmetry, and a direction of opening based on the sign of the leading coefficient.

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