Lesson 1

Discover

 

The vertex form of a quadratic function was introduced in Focus. In this Discover section you will investigate the effects of changing the values of a, q, and p in the equation y = a(x − p)2 + q.

 

Try This 1

 

Open Quadratic Function (Vertex Form).

 

 

Part A: Investigation of a

1. Use the a-slider to explore how the value of a in y = ax2 changes the shape of the graph. Make sure the parameters p and q are set to 0. You may use a chart similar to the one shown to record your observations.
   
   
    

   a	y = ax2	Observations or Sketch
   9	y = 9x2
   2	y = 2x2
   1	y = 1x2
   0.5	y = 0.5x2
   0.2	y = 0.2x2
   −0.2	y = −0.2x2
   −0.5	y = −0.5x2
   −1	y = −1x2
   −2	y = −2x2
   −9	y = −9x2

   
   
   

Part B: Investigation of q

2. Use the q-slider to explore how the value of q in y = x2 + q  changes the position of the graph. Make sure the parameter a is set to 1 and p is set to 0. You may use a chart similar to the one shown to record your observations.
   
   
    

   q	y = x2 + q	Observations or Sketch
   6	y = x2 + 6
   3	y = x2 + 3
   0.5	y = x2 + 0.5
   0	y = x2
   −0.5	y = x2 − 0.5
   −3	y = x2 − 3
   −6	y = x2 − 6

   
   
   

Part C: Investigation of p

3. Use the p-slider to explore how the value of p in y = (x − p)2  changes the position of the graph. Make sure the parameter a is set to 1 and q is set to 0. You may use a chart similar to the one shown to record your observations.
   
   
    

   p	y = (x − p)2	Observations or Sketch
   6	y = (x − 6)2
   3	y = (x − 3)2
   0	y = x2
   −3	y = (x + 3)2
   −6	y = (x + 6)2

   
   

Save your responses in your course folder.