Students

Learning Objective: SWBAT explain the meaning of the terms in a quadratic expression that represents the height of a falling object, and use tables and graphs to represent this equation and situation.

Online Resource: https://www.desmos.com/calculator/07jbrmkfny

Instructions: You drop a ball from the roof of a building and watch in fall to the ground. The function f(t) = at2+c represents the height of the ball in terms of seconds, t. Right now a = -16 and c = 400. Use the sliders to see what happens when you change the value of a and c.

What happens when you increase the value of a? What happens when you decrease the value of a? What happens when you increase the value of c? What happens when you decrease the value of c? What do you think a represents in this situation? What do you think c represents in this situation?

Learning Objective: SWBAT create quadratic functions and graphs that represent a situation.

Online Resource: https://www.desmos.com/calculator/tcjfn7pqsr

Instructions: Part 1: You throw a ball up in the air and watch it fall back down. The function f(t) = at2+ bt + c  represents the height of the ball in terms of seconds, t. Right now a = -16, b = 90, and c = 5. Use the sliders to see what happens when you change the values of a, b, and c.

Work with your groups

What happens when you increase the value of a? What happens when you decrease the value of a? What happens when you increase the value of b? What happens when you decrease the value of b? What happens when you increase the value of c? What happens when you decrease the value of c? What do you think a represents in this situation? What do you think b represents in this situation? What do you think c represents in this situation?

Part 2: You dive off the diving board, first going up, and then down into the water. Write a function in the form f(t) = at2+ bx + c to represent this situation. What does a represent? What does b represent? What does c represent? Graph your function on desmos.

Learning Objective: SWBAT model a real-world scenario with quadratic functions and graphs and analyze the vertex of a graph and the zeros of the function in context.

Online Resource: https://www.desmos.com/calculator/57jfurljci

Instructions: Part 1: You throw a ball up in the air and watch it fall back down. The function f(t) = at2+ bx + c  represents the height of the ball in terms of seconds, t. Right now a = -16, b = 90, and c = 5. 

Work with your group:

What are the coordinates of the vertex of this function? What does it mean in context? What are the coordinates of the x-intercept? What does it mean in context?

Part 2: Use the slider to change the value of b. What did you change it to? What is your new vertex? What is your new x intercept? What does this mean in context?

Part 3: Use the slider to change the value of c. What did you chant it to? What is your new vertex? What is your new x intercept? What does this mean in context?