Lesson 2

Lesson 2: Quadratic Function in Vertex Form

Focus

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A batter really focuses on the path of a baseball once the ball leaves the pitcher’s hand. The batter has only a fraction of a second to predict the ball’s speed and path and must decide whether or not to swing. If the batter decides to swing, she or he must predict where the ball will be so the ball can be connected with the bat at the right place and angle. The ball’s path can be accurately described mathematically using a quadratic function.

In this lesson you will learn how to describe the coordinates of the vertex of a quadratic function and find the x- and y-intercepts of the graph. You will not only learn how to sketch a graph from the equation, but you will also learn how to determine the equation from the characteristics of the graph. Doing so will allow you to comfortably predict the path of a baseball or other projectile, such as the water needed for your Module 3 Project.

Outcomes

At the end of this lesson you will be able to

• identify and verify the coordinates of the vertex for a quadratic function of the form y = a(x − p)2 + q and write a rule describing how to do so
  
  
• sketch the graph of y = a(x − p)2 + q using transformations; and identify the vertex, domain and range, direction of opening, axis of symmetry, and x- and y-intercepts
  
  
• explain, using examples, how the values of a and q may be used to determine whether a quadratic function has zero, one, or two x-intercepts
  
  
• write a quadratic function in the form y = a(x − p)2 + q for a given graph or a set of characteristics of a graph

Lesson Questions

You will investigate the following questions:

• How can you sketch a graph of a quadratic function knowing the a-, p-, and q-values?
  
  
• How can you write an equation for a quadratic function from its graph?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 2 Assignment (Download the Lesson 2 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 3 Glossary Terms and Formula Sheet
  
  
• work under Project Connection

Materials and Equipment

You will need graph paper.