1. 5.7 Curve Fitting with Quadratic Models Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. Warm-up (IN)

2. Notes Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. There are 2 ways to fit a curve to a set of data points - 1 – enter data into lists on calc, the find quadreg 2 – use a system of equations Ex 1 – Find a quadratic function whose graph contains the points (-3,16), (2,6) and (1,-4) Step 1 Write a system of 3 equations in 3 variables using (-3,16) (2,6) (1,-4)

3. Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. Step 2 Use matrices to solve the system for a, b and c (3,1,-8)

4. Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. Ex 2 – On a trip to St. Louis you visit the Gateway Arch. Since you have plenty of time on your hands, you decide to estimate its height. You walk the distance across the base of the arch and find that it is 162 meters. You assume the arch is in the shape of a parabola and you set up a coordinate system with one end of the arch at the origin. To find a third point, you measure the vertical distance to the arch is 4.55 meters when you are one meter from the base. (0,0) (162,0) (1,4.55)

5. (0,0) (162,0) (1,4.55) Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model to represent a data set. (-0.03,4.58,0) Use calc to find max! 174.8 meters

6. HW – Out – Explain why you can always find a quadratic functi0n to fit any three noncollinear points in the coordinate plane. Summary – I can use this when I… POW!!