AFDA Unit 4: Quadratic Functions Day 7 Notes: Quadratic Formula and Regression Name: Block: Date: Today you will be using the Discriminant to determine the number and type of solutions for a quadratic function Quadratic formula to solve quadratic functions review correlational vocabulary learn how to run quadratic regressions in the calculator The Discriminant and Quadratic Formula: Standard form: aaxx 2 + bbbb + cc = 0 Positive: Equals Zero: Negative: Directions: Find the discriminant of the following problems and state the nature and the number of solutions. Use the quadratic formula to determine the solutions and draw a quick sketch of the graph. xx 2 8xx + 16 = 0 5xx 2 + xx + 1 = 0 8xx 2 + 8xx + 3 = 0 aa = bb = cc = aa = bb = cc = aa = bb = cc = Discriminant and # of Solutions Discriminant and # of Solutions Discriminant and # of Solutions
xx 2 8xx + 16 = 0 5xx 2 + xx + 1 = 0 8xx 2 + 8xx + 3 = 0 Quadratic Formula Quadratic Formula Quadratic Formula Rough Sketch of Graph Rough Sketch of Graph Rough Sketch of Graph Quadratic Regression: Domain: : prediction of data within the data set Range: : prediction of data outside the data set Correlation (r) - of a relationship between paired data (two variables). It can be strong/weak, negative/positive.
New! Coefficient of Determination represents the of data that is closest to the regression curve of best fit. Symbolized as or. o Value is 0 rr 2 1 If rr 2 = 0.850 then data fits the regression curve. The closer to 1, the better the fit. Practice 1: The following table shows the concentration in milligrams per liter of a medication in patient s blood as time passes. Time (hours) 0 0.5 1 1.5 2 2.5 Concentration (mg/l) 0 78.1 99.8 84.4 50.1 15.6 a. Enter the data in your calculator (press STAT, choose 1:Edit, x-values go in L1 and y-values go in L2), look at the scatterplot (press graph), and describe any patterns. b. Determine the equation of LINEAR regression (STAT, CALC, 4:LinReg [ax+b]) Round to three decimals. What is the r value (round to three decimals)? What does this mean? What is the rr 2 value (round to three decimals)? What does this mean? c. Determine the equation of the QUADRATIC regression (STAT, CALC, 5:QuadReg). Round to three decimals. What is the rr 2 value? What does this mean? Round to three decimals. d. Which model is a better fit for the data? Why? e. Using the better regression model and table function, what is the concentration of medicine in the patient s blood after 4 hours? Is this interpolation or extrapolation?
f. What is the practical domain and practical range of the regression function? What does this mean? Round to one decimal for both domain and range. Practice 2: The total sales, s, of TV antennas for various years from 1980 to 1995 are shown in the table below, where t=0 represents the year 1980. Sales are show in millions of dollars. Time, t 2 5 7 13 15 Sales (in millions of USD), s 76.3 82.2 84.6 80.9 77.3 a. Enter the data in your calculator, look at the scatterplot, and describe any patterns. b. What is the equation of the regression model of best fit? Round to three decimals. What is the rr 2 value? What does this mean? Round to three decimals. c. Using the regression model and table feature, determine in what year sales reach their maximum. d. Use the regression model and table feature to estimate the total sales of TV antennas for 2008. Round to one decimal. e. What is the practical domain and range of the regression function? What does this mean? Round to the nearest whole number for domain and one decimal for range. General Set-up - only do at the beginning not necessary to do each time
xx 11 1. Press 22 nnnn 0 2. Press 3. Scroll to find DiagnosticOn 4. Hit ENTER twice 5. Press Y= to make sure Y1 is empty and Plot1 is highlighted Entering Data/Viewing Graph 1. Press STAT and select 1: Edit 2. Enter data in L1 and L2 3. Press ZOOM and select 9:ZoomStat 4. Based on graph behavior and shape, determine which regression to run *This graph in particular looks to be increasing linear* Calculating Regression Equation
1. Press STAT, scroll to the right for the CALC menu 2. Based on graph behavior and shape, run the corresponding regression. Move cursor down to Store Reg EQ: 3. Press VARS 4. Scroll right to Y-VARS menu and select 1:Function 5. Select 1: Y1 6. Scroll to Calculate and hit ENTER 7. Use the given information to write the equation of the line. **If the rr 2 value does not appear, then reference General Set-up to turn Diagnostic On Types of Regressions: *Rounded to 3 decimals the regression equation is: yy = 523.561xx + 5754.428 4:LinReg (ax+b) for linear 5:QuadReg for quadratic 6:CubicReg for cubic 7:QuartReg for quartic 9:LnReg for natural logarithmic 0:ExpReg for exponential