1 / 7

Quadratic Application Problems

This lesson focuses on applying quadratic equations to real-world problems, specifically modeling the motion of a ball thrown into the air. We analyze the scenario of a ball thrown from a height of 3 feet with an initial velocity of 14 ft/sec and the effect of gravity. Students will derive the quadratic equation, find its roots, and determine key attributes such as height after given time, how long it takes to hit the ground, and the maximum height reached. Various methods including factoring and the Quadratic Formula will be utilized for problem-solving.

cian
Download Presentation

Quadratic Application Problems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Quadratic Application Problems Algebra Unit 11

  2. Quadratic Application Problems If an object is tossed into the air… • the path of the object is represented by the equation at2+ bt+ c = h • where h is the height after tseconds • ais the acceleration due to gravity • bis the initial velocity • cis the initial height

  3. modeling A ball is thrown straight up, from 3 ft above the ground, with an initial velocity of 14 ft/sec. It’s the acceleration due to gravity is -5 ft/sec. Use the equation at2 + bt + c = h Use any method to solve for t (factoring, Quadratic Formula, square roots). A) Write the quadratic equation representing this scenario when h= 0. B) Find the roots (solutions) for this quadratic equation. -15 -1 15 14

  4. modeling A ball is thrown straight up, from 3 ft above the ground, with an initial velocity of 14 ft/sec. It’s the acceleration due to gravity is -5 ft/sec. Substitute 2 seconds for t and solve for h. Recall the roots (solutions) you already found. Which one makes sense? C) How high will the ball be after 2 seconds? h = 11 feet after 2 seconds D) How long will it take for the ball to hit the ground?

  5. y x modeling Find the vertex of the parabola. Find the y – intercept. Then reflect that point across the axis of symmetry. Plot the x – intercepts . Draw a smooth curve connecting the points. E) Graph Thus the vertex is (1.4 ,12.8). Graph applied to problem means that the graph starts at (0,3). y – intercept (–0.2 ,0) (3,0) x – intercepts

  6. Modeling F) Using the graph, what is the maximum height the ball reaches? The maximum height the ball reaches is the y– value of the vertex. Since the vertex is (1.4 ,12.8), the ball reaches a maximum height of 12.8 feet.

  7. independent practice Begin Homework: Worksheet

More Related