Lesson 3

Self-Check 1

1. Complete the square and convert the following quadratic functions to vertex form.
   
   
   1. y = x2 + 10x + 20 Answer
      
      
   2. f(x) = x2 − 8x − 2 Answer
      
      
   3. y = 3x2 + 12x + 7 Answer
      
      
   4. f(x) = −4x2 + 24x − 30 Answer

2. Identify two errors in the following completing-the-square sequence.
   
   
    
   
   
   Answer
   
   
3. Convert the following functions to the vertex form, and then describe the graphs based on what you learned in Lessons 1 and 2. Explain how you know the characteristics of the graphs. Put the functions into a graphing calculator or use Quadratic Function (Vertex Form) to check your result.
   
   
    
   
   
   
   
   1. y = 3x2 − 30x + 77 Answer
      
      
   2. y = −2x2 − 24x − 69 Answer

Try This 3

Graph the functions in both the vertex form and the standard form to check that your work is correct. If your graphs are exactly the same, you have completed the square correctly!

1. Take the two forms of the quadratic function in Self-Check 1 question 3.a., y = 3x2 − 30x + 77 and y = 3(x − 5)2 + 2. Verify that both forms are the same function by graphing each form on a graphing calculator.
   
   Here’s how to use your graphing calculator:
   
   
   • Press the “Y=” key at the top and enter the standard form of the function in the “Y1=” field.
     
     
      
     
     
     
   • Press “ENTER” or the down arrow to go to the next line.
     
     
   • Enter the vertex form of the function in the “Y2=” field.
     
     
      
     
     
     
   • Press the “GRAPH” key. The calculator will draw the graphs of the two functions. If the two functions are the same, you will only see one parabola. If you see two parabolas, then you have not completed the square correctly.
     
     
      
     
     
     

2. Take the two forms of the quadratic function in Self-Check 1 question 3.b., y = −2x2 − 24x − 69 and y = −2(x + 6)2 + 3. Verify that both forms are the same function by graphing each form on a graphing calculator.
   
   If you have trouble inputting the equations, consult your teacher or another student who knows how to perform this sequence. You will use this graphing skill again and again.

   
   If you have used an online graphing tool, save screenshots of your work in your course folder.