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6 minutes Warm-Up 1) Write the system of equations represented by 2 2 x 16 1 3 y 4 2) Write the matrix equation that represents x y 6 2x 4 3) Find the inverse of 3 1 4 2 5.7 Curve Fitting With Quadratic Models Objectives: •Find a quadratic function that exactly fits three data points •Find a quadratic model to represent a data set Example 1 Find a quadratic equation whose graph contains the points (-3,16), (2,6), and (1,-4). Step 1: Write a system of equations in three variables y = ax2 + bx + c Point Substitution Equation (-3,16) a(-3)2 + b(-3) + c = 16 9a – 3b + c = 16 (2,6) a(2)2 + b(2) + c = 6 4a + 2b + c = 6 (1,-4) a(1)2 + b(1) + c = -4 a + b + c = -4 Step 2: Use a matrix equation to solve the system 9 3 1 a 16 4 2 1 b 6 1 1 1 c 4 Example 1 Find a quadratic equation whose graph contains the points (-3,16), (2,6), and (1,-4). Step 2: Use a matrix equation to solve the system 9 3 1 a 16 4 2 1 b 6 1 1 1 c 4 Step 3: Write the quadratic equation Example 2 Find a quadratic model to represent the data in the table below. Step 1: Enter the data and make a scatter plot Step 2: Use the quadratic regression feature to find a quadratic model y = 0.008x2 + 0.518x + 131.886 x y 25 50 150 178 75 100 216 265 125 150 175 323 392 470.4 Homework workbooks p.33 #1,7,13-17