Lesson 4

Lesson 4: Vertex Form of Quadratic Functions

 

Focus

 

Riding a snowmobile in winter can be a great activity. Running your snowmobile up a slope, jumping it into the air, and landing in soft snow can be very exhilarating. It is like producing your own carnival ride. Competitions are sometimes held to see who can jump the farthest or the highest. The path of the snowmobile can be modelled and predicted using quadratic functions. What is learned from these functions can guide riders to greater lengths or heights in a jump.

 

Up to this point in the module, you have usually worked with the standard form of the quadratic function. You have seen it written as y = ax2 + bx + c. You may have also seen it written as f(x) = ax2 + bx + c, which is known as function notation. The standard form of the quadratic function is very useful in predicting the initial height of projectiles and modelling other real-life situations. This is because the constant c in the function is always the y-intercept of the graph.

 

In this lesson you will encounter the vertex form of the quadratic function: y = a(x − h)2 + k. In both the standard form and the vertex form, there is a variable raised to the second power and the highest power of a variable is 2, so it is easy to recognize them as quadratic functions.

 

The vertex form is excellent for modelling situations where the maximum or minimum value is important. The vertex form enables you to know the maximum height of a jump more easily than the standard form of a quadratic function does. In this lesson you will learn to model situations and solve problems using the vertex form of the quadratic function as well as the standard form.

 

Lesson Questions

 

In this lesson you will investigate the following inquiry questions:

• How is the graph of a quadratic function affected by a change in the constants a, h, and k in the vertex form, y = a(x - h)2 + k?
  
  
• How do you convert from vertex form to standard form and back?
  
  
• How do you solve problems using a quadratic function in vertex form?

Assessment

• Lesson 4 Assignment

All assessment items you encounter need to be placed in your course folder.

 

 

Save a copy of the Lesson 4 Assignment to your course folder. You will receive more information about how to complete the assignment later in this lesson.

 

 

Materials and Equipment

• graphing calculator