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College Algebra Math 130

College Algebra Math 130. Amy Jones Lewis. Kicking a Soccer Ball.

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College Algebra Math 130

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  1. College AlgebraMath 130 Amy Jones Lewis

  2. 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.

  3. 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.

  4. 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?

  5. 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?

  6. 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.

  7. Homework Solve the following quadratic equations. x2 + 7x – 2 = 0 -3x2 + 4x – 8 = 0 Next Class: Thursday, November 18

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