7.2 Write Quadratic Functions and Models 7.2 HW Quiz: Sept. 15 (Wednesday) 7.1-7.2 Quiz: Sept. 17 (Friday) 7.1,7.2,7.7 Test: Sept. 22 (Wednesday)

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7.2 Write Quadratic Functions and Models 7.2 HW Quiz: Sept. 15 (Wednesday) Quiz: Sept. 17 (Friday) 7.1,7.2,7.7 Test: Sept. 22 (Wednesday)

Vocabulary  Quadratic Regression: the process of finding the best-fitting quadratic model for a set of data  Curve Fitting: find a line or curve that matches a set of data points

Quadratic Regression  The table shows the population of a bacteria culture from day 5 to day 30. Use a graphing calculator to find the best-fitting quadratic model. (quadratic regression) Day Population

Quadratic Regression y = 0.66x x Standard Form

You Try:  Use a graphing calculator to find the best- fitting quadratic model for the given values: (4, 56), (8, 100), (12, 165), (16, 255), (20, 360), (24, 500) y = 0.714x x + 37

Transformations a = vertical shrink / stretch by a (h, k) = vertex of parabola (x, y) = point on parabola (there are infinitely many!!) p, q = x-intercepts of parabola

You Need to know these forms for Quadratic Functions:  Vertex Form: (h, k) represent the vertex y = a(x – h) 2 + k  Intercept Form: p and q represent intercepts on the x-axis y = a(x – p)(x – q)  Standard Form: y = ax 2 + bx + c

y = 2(x + 2) 2 – 3 They are giving you the vertex and a point…use VERTEX FORM!

– 2 1 y = 1(x + 3)(x – 2) They are giving you the intercepts and a point…use INTERCEPT FORM!

Homework – Start NOW!  P. 257 #1-10, #17-20