Vertex Form Applications Grade: 11 Subject: Pre- Calculus 11 Unit: Quadratics Driving Question: Bill kicks a football in Tom s direction. The football follows a parabolic path. Tom is unaware that he may be standing in the football s path. After having traveled a horizontal distance of 10 metres, the football reaches a maximum height of 18 metres. Will the football hit Tom, who is 1.8 metres tall, if he s standing 1 metre from the spot where the football should hit the ground? Curriculum Outcomes: GCO s SCO s Students will be expected to develop algebraic and graphical reasoning through the study of relations. RF03: Analyze quadratic functions in vertex form and determine the vertex, domain and range, direction of opening, axis of symmetry, and x and y intercepts. RF05: Solve problems that involve quadratic equations.
Screencast Link(s): Vertex Form Applications: https://www.youtube.com/watch?v=z7isrhjbk9e Quadratic Formula: https://www.youtube.com/watch?v=ogu_odvi_ka Expected Time: 2 classes Resources: (Tools & Tech) Lesson Procedure We do: Desmos.com Can be accessed using laptops or hand held device. Teacher to run activity from Desmos.com: Polygraph: Quadratics Students to log into student.desmos.com and enter pin provided from teacher computer. Students will be randomly paired by the program and play a Guess Who? type activity in which they will use their knowledge of the characteristics of quadratic functions to narrow done the parabola selected by their partner. This activity will serve as a review of prior knowledge of quadratics and reinforce the correct use of terminology. Access to device for watching screencast videos I do: Teacher to introduce the driving questions. Students will be assigned groups of 3 to work on the driving question. This question is an application of previously studied concepts. Students can pre- watch the videos as a review of the concept or watch as a group at the beginning of class. We do: Work as a group to solve the driving question. Solution should be presented in a format in which all calculations and rational for work is clearly provided. Groups will present their solutions to the class.
We share: 2 groups to be randomly selected to present their solution at the end of class. Teacher to lead a discussion providing feedback and offering feedback and answering questions that arise. You do: Work on applications problem worksheet as preparation for activity next class. I do: Teacher to close class assigning particular questions from worksheet for homework based on progress of students. Question #5 must be included in assigned questions as it will serve as an introduction to the next activity. Student Worksheets: Vertex Form Application Questions
VERTEX FORM APPLICATION QUESTIONS 1. Suppose a parabolic archway has a width of 280 cm and a height of 216 cm at its highest point above the floor. Write a quadratic function in vertex form that models the shape of this archway. 2. The deck of the Lion s Gate Bridge in Vancouver is suspended from two main cables attached to the tops of two supporting towers. Between the towers, the main cables take the shape of a parabola as they support the weight of the deck. The towers are 111 m tall relative to the water s surface and are 472 m apart. The lowest point of the cables is approximately 67 m above the water s surface. Model the shape of the cables with a quadratic function in vertex form. 3. During a game of tennis, Josie hits the tennis ball into the air along a parabolic trajectory. Her initial point of contact with the tennis ball is 1 m above the ground. The ball reaches a maximum height of 10 m before falling toward the ground. The ball is again 1 m above the ground when it is 22 m away from where she hit it. Write a quadratic function to represent the trajectory of the tennis ball if the origin is at the spot above the ground from which the ball is hit. 4. Water is spraying form a nozzle in a fountain, forming a parabolic path as it travels through the air. The nozzle is 10 cm above the surface of the water. The water achieves a maximum height of 100 cm above the water s surface and lands in the pool. The water spray is again 10 cm above the surface of the water when it is 120 cm horizontally from the nozzle. Write the quadratic function in vertex form to represent the path of the water if the nozzle is considered the origin.
5. a) Write quadratic functions in vertex form that represent three different trajectories the basketball shown can follow and pass directly through the hoop without hitting the backboard. b) Which of your three quadratic functions do you think represents the most realistic trajectory for an actual shot? Explain your thoughts.