2, Fall 2017-2018 Exercise 1. Use the FOIL to expand the following: 1. (4 y8)(3 y +7) 2. (4 w8)(w+3) 3. (x5)(x +5) 4. (2 x + 4) 2 Exercise 2. Solve the following equations (you can use any method of solving quadratic equations) 2 1. ( y3) =64 2. 4 x 2 +11=59 3. x + 8 x +16=49 4. ( 2 x5 )2=49 2 Exercise 3. Solve for x in each of following equations (Rational Equations by Cross Multiplying) 1. x 7 = 9 3 2. x5 4 = 15 5 3. 3 x +1 =5 x1 4. x6 2 x2 = 3 15 1 Exercise 4 Ellen and Kelly test Ellen's new car in an empty parking lot. They mark a braking line where Ellen applies the brakes. Kelly then measures the distance from that line to the place where Ellen stops, for speeds from 5 miles per hour to 25 miles per hour. Brake Test Speed (mi/h) 5 10 15 20 25 Stopping Distance (ft) 7 17 30 46 65 Ellen wants to know the stopping distance at 60 miles per hour. She cannot drive the car at this speed in the parking lot, so they decide to try curve fitting, using the data they have collected. Can you use a quadratic function to represent the data in the table? Explain how you know. _____________________________________________________________________________________ ______________________________________________________________________________________ Exercise 5 (Finding the quadratic equation given three points) Given the three points (0, 5), (2, 1) and (3, 2), follow the steps below to find the corresponding quadratic equation. a. Use the three points to write a system of equations to find a , b , and c in f ( x)=a x 2 +bx +c b. Use any method to solve 3 equations with 3 variables. Find the values for a , b , and c c. Write the quadratic function. 2