7.2 Writing Quadratic Functions and Models

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7.2 Writing Quadratic Functions and Models What do you call 2 quadratics who like to go bowling? A para-bolas

Bacteria Growth Which is a Better Fit? Day (X): Population (Y): 5 10 15 20 25 30 60 135 240 370 500 740

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

Back to Bacteria Standard Form:

You Try: (QuadReg) (Txtbk p. 256 GP #7) Enter Data L1, L2 STATPLOT “On” (Scatterplot) L1, L2 ZOOM 9 STAT > CALC > 5: GRAPH (VARS, etc.)

A Parabola in Vertex Form: y = a (x - h)2 +k What variations of a parabola are there?

Write EQ Given Vertex & Point: y = a(x - h)2 +k Substitute in everything and get “a”! Then rewrite the equation with x and y (numbers for a, h, k). Ex: Vertex (-2, 1), point (2, 5)

y = a(x – h)2 + k Write a quadratic function in vertex form EXAMPLE 1 Write a quadratic function for the parabola shown. SOLUTION Use vertex form because the vertex is given. y = a(x – h)2 + k A quadratic function for the parabola is y = (x – 1)2 – 2.

GUIDED PRACTICE Write a quadratic function whose graph has the given characteristics. 1. vertex: (4, –5) passes through: (2, –1) y = (x – 4)2 – 5 ANSWER 2. vertex: (–3, 1) passes through: (0, –8) ANSWER y = (x + 3)2 + 1

Homework See Agenda