ALGEBRA 2 5.8: Curve Fitting With Quadratic Models

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Presentation transcript:

ALGEBRA 2 5.8: Curve Fitting With Quadratic Models

Finite Differences When you have a set of data that has the x’s equally spaced, you can use finite differences to find out what type of equation would best fit it. 1st differences are constant = Linear 2nd differences are constant = Quadratic 1 2 3 4 5 -2 6 1 2 3 4 5 10 17

Ex 1: Determine whether each data set could represent a quadratic function. Explain A) B) x 1 3 5 7 9 y -1 17 31 x 3 4 5 6 7 y 1 9 27 81

Use Matrices to Write a Quadratic Function Need 3 points Use ax2 + bx + c = y to plug in x’s and y’s Use inverse or augmented matrices and calculator to solve for a, b, and c (1,-1) (3, 1) (5, 7)

Short way to set up the matrices. Ex 2: Find a quadratic equation that fits the points (1, -5) (3, 5) and (4, 16)

Quadratic Regression Can use the calculator to estimate a quadratic equation through a set of data Steps Enter data in lists (stat, edit) Make sure diagnostic is on (catalog) Run a quadratic regression (stat, calc, QuadReg) You can plot data and graph equation to see how it fits r tells you how well it fits the data

Ex 3: The table shows the cost of circular plastic wading pools based on the pools’ diameter. Find a quadratic model for the cost of a pool, given its diameter. Use the model to estimate the cost of a pool with a diameter of 8 ft. Diameter (ft) Cost 4 $19.95 5 $20.25 6 $25.00 7 $34.95

Assignment #8 page 377 #’s 12-19,(58)