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Quadratic Functions and Models Lesson 3.1

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Nonlinear Data When the points of the function are plotted, they do not lie in a straight line. This graph contains points from a quadratic function of the form Contrast to linear

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General Form Quadratic functions have the standard form y = ax 2 + bx + c a, b, and c are constants a ≠ 0 (why?) Quadratic functions graph as a parabola

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Axis of Symmetry Parabolas are symmetric about a vertical axis For y = ax 2 + bx + c the axis of symmetry is at Given y = 3x 2 + 8x What is the axis of symmetry?

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Vertex of the Parabola The vertex is the “point” of the parabola The minimum value Can also be a maximum What is the x-value of the vertex? How can we find the y-value?

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Vertex of the Parabola Given f(x) = x 2 + 2x – 8 What is the x-value of the vertex? What is the y-value of the vertex? The vertex is at (-1, -9)

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Vertex of the Parabola Given f(x) = x 2 + 2x – 8 Graph shows vertex at (-1, -9) Note calculator’s ability to find vertex (minimum or maximum)

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Other Quadratic Forms Standard form y = ax 2 + bx + c Vertex form y = a (x – h) 2 + k Then (h,k) is the vertex Given f(x) = x 2 + 2x – 8 Change to vertex form Hint, use completing the square

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Identifying Quadratic Functions How can you determine which of the following is quadratic or not? What determines whether a parabola opens down or up?

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Assignment Lesson 3.1A Page 183 Exercises 1 – 77 EOO

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Modeling Quadratic Data Consider the following table … Is it linear or non linear? Graph the data on your calculator

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Modeling Quadratic Data The calculator can do quadratic regression to find a modeling function While in the data matrix mode Press F5, then specify QuadReg Fill in remaining parameters as specified here.

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Modeling Quadratic Data Note results Formula Graph

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Assignment Lesson 3.1B Page 185 Exercises 97 – 109 EOO

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