Big ideas math algebra

Question

The path of a ball kicked from the ground can be modeled by the equation y= -1/5 (x-5)(x-20), where x and y are measured in feet. the x-axis represents the ground. How far does the ball land from where it’s kicked?

Answer 1

This question can be answered with the use of a Ti84 graphing calculator. Simply enter this equation in Y=, graph it, and determine the zeroes. This can done because the ball is on the ground whenever y=0 as y represents the height of the ball. The distance between the two zeroes is how far the ball has traveled from when it is kicked to when it lands.

Alternatively, this problem can be done algebraically. 20 and 5 are the roots of this equation. The equation presented to us is already factored, so in order to determine the roots of this equation, each factor should be set equal to 0 and the solved. 20-5=15, therefore the ball has traveled 15 feet.