College Algebra Math 130 Amy Jones Lewis Kicking a Soccer Ball A friend of yours is working on a project that involves the path of a soccer ball. She tells you that she has collected data for several similar soccer kicks in a controlled environment (with no wind and minimum spin on the ball). She has modeled the general path of the ball using a quadratic function. Kicking a Soccer Ball Your friend’s model is y = -0.01x2 + 0.6x where x is the horizontal distance that the ball has traveled in meters and y is the vertical distance that the ball has traveled in meters. Complete a table of values that shows the vertical and horizontal distances that the ball has traveled. Can you approximate from your table how far the ball traveled before it hit the ground? If so, describe the distance. Graph the function on your calculator – be sure to include the full path of the soccer ball in your window. Kicking a Soccer Ball What is the vertex of the parabola? Is it a maximum or a minimum? What is the y-intercept of the graph? What does it represent in this problem situation? How far does the ball travel horizontally before it hits the ground? What does this point represent on the graph? Kicking a Soccer Ball Write an equation that you can use to algebraically find the answer to the question about the ball hitting the ground. Can you visually determine the solutions to this equation? To solve the equation in the previous question, we can use the Quadratic Formula. Can you find the solutions to the equation 2x2 – 3x + 1 = 0? Kicking a Soccer Ball For each quadratic equation below, find the values of a, b, and c. 5x2 + 6x + 1 = 0 8x2 + 4x – 6 = 0 10x2 – 1 = 0 -x2 + 8x = 2 Find the solutions to the equations. Use the Quadratic Equation to find the horizontal distance that the ball travels before it hits the ground. Homework Solve the following quadratic equations. x2 + 7x – 2 = 0 -3x2 + 4x – 8 = 0 Next Class: Thursday, November 18

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