Math Problem Statement

A soccer ball is kicked fromSoccer Ball Height Calculation the ground and follows a parabolic path. The path is given by y = -1.6x^2 + 4.48x, where x is the horizontal distance the ball has traveled and y is the vertical height of the ball in meters. Which of the following would represent the height of the ball before it is kicked?

Solution

To determine the height of the soccer ball before it is kicked, we need to evaluate the given equation y=1.6x2+4.48xy = -1.6x^2 + 4.48x at x=0x = 0, because xx represents the horizontal distance the ball has traveled, and the ball has traveled no distance horizontally when it is initially kicked.

Substituting x=0x = 0 into the equation:

y=1.6(0)2+4.48(0)y = -1.6(0)^2 + 4.48(0)

y=0y = 0

Thus, the height of the ball before it is kicked is 0 meters, meaning the ball starts on the ground.

Would you like further details or additional assistance?

Related Questions:

  1. What does the vertex of this parabola represent in the context of the problem?
  2. How can you determine the maximum height of the ball?
  3. What is the horizontal distance traveled when the ball reaches its maximum height?
  4. How do you calculate the total distance the ball travels before hitting the ground again?
  5. How does changing the coefficients of x2x^2 and xx affect the path of the ball?

Tip:

When solving parabolic equations, evaluating at x=0x = 0 often reveals the starting value, which is useful for interpreting initial conditions.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Parabolas
Initial Conditions

Formulas

y = ax^2 + bx + c

Theorems

Zero Property for Quadratic Equations

Suitable Grade Level

Grades 9-10