Lesson 5

Quadratic functions can be represented in three forms:

• standard form, y = ax2 + bx + c
• vertex form, y = a(x − h)2 + k
• factored form, y = a(x − r)(x − s)

In this lesson you saw how the standard form of a quadratic function can be written in factored form. In Lesson 4 you learned how to convert vertex form to standard form.

Share 1

With another student or appropriate partner, complete the following activity.

• Enter the following quadratic function into your calculator: y = −2(x + 1)2 + 8.
  
  
• Write the function y = −2(x + 1)2 + 8 in standard form.
  
  
   
  
  
  Enter this standard form of the function into your calculator in Y2.

• From the standard form of the function, determine the factored form of the function and enter it into your calculator in Y3.
  
  
   
  

• Press GRAPH.

With your partner, discuss how many graphs are displayed and give an explanation for what you see.

Each form of a quadratic function provides information about the graph of the function. The graph of a function can be sketched more easily from the vertex form. So, which form of the quadratic function should you use to solve contextual problems?

• Use the vertex form if you want to know the maximum or minimum value.
• Use the standard form if you want to know the y-intercept.
• Use the factored form if you want to know the x-intercepts.