4.1 Day 2: Graphing Quadratic Functions Agenda: 4.1/4.7 Foldable Check Homework 4.1 Day 2 Notes

Check Homework

Check Homework

Example 1 The path of a diver is approximated by feet in the figure shown and the equation given. What is the maximum height of the diver? Approximately how long did it take the diver to reach his maximum height?

Example 2 The Empire State Building is 1250 feet tall. If an object is thrown upward from the top of the building at an initial velocity of 38 feet per second, its height s seconds after it is thrown is given by the function ℎ 𝑥 =−16 𝑠 2 +38𝑠+1250. How high does the ball go in the air?

Example 3 A juggler throws a ball in the air, releasing it 5 feet above the ground with an initial velocity of 15 ft/sec. She catches the ball with her other hand when the ball returns to 5 feet above the ground. If the equation ℎ=−16 𝑡 2 +15𝑡 give the path of the ball from hand to hand, find how height the ball gets in the air.

Brain Break As a class we are going to try to reach 21 by counting. Here’ s the catch. You have to close your eyes in order to play. You are only allowed to say one number and only one person can say a number at a time.

Example 4 When a gray kangaroo jumps, its path through the air can be modeled by 𝑦=−0.0267 𝑥 2 +0.8𝑥 where x is the kangaroo’s horizontal distance traveled in feet and y is its corresponding height in feet. How high can a gray kangaroo jump?

Example 5 A firework is shot upward so that it follows the equation y = -16x2 + 80x + 3 where y is the height of the firework and x is time. How high does the firework climb before it starts to descend?

Example 6 An owl is circling a field at a height of 100 ft. and sees a mouse. The owl dives to catch the mouse along the path y = 16x2 + 10x + 100. How low does the owl need to dive to capture the mouse?