Lesson 5

Try This 1

Use Factored Quadratic to draw graphs of the following quadratic functions and answer the associated questions.

1. In the applet, draw the quadratic function f(x) = 4x2 + 4x − 24 by moving the slider to change the values for a, b, and c.
   
   
   1. What are the x-intercepts for the graph? Answer
    
   2. How many x-intercepts are there? Answer

2. The factored form of the function in question 1 is f(x) = 4(x + 3)(x − 2).
   
   
   1. What are the values of r and s? Answer
    
   2. How do the values of r and s relate to the x-intercepts for the graph? Answer
    
   3. From the graph, what is the y-intercept of the graph? Answer
    
   4. Calculate the y-intercept using the formula y = ars. Answer

3. Draw the quadratic function f(x) = −3x2 + 6x − 3.
   
   
   1. What are the x-intercepts for the graph? Answer
    
   2. How many x-intercepts are there? Answer

4. The factored form of the function in question 3 is f(x) = −3(x − 1)(x − 1), which can also be written as f(x) = −3(x − 1)2.
   
   
   1. What are the values of r and s? Are they different numbers in this case? Answer
    
   2. How do the values of r and s relate to the x-intercepts for the graph? Answer
    
   3. What is the y-intercept of the graph? Answer
    
   4. Calculate the y-intercept using the formula y = ars. Answer

5. A quadratic function is written as f(x) = 2x2 + 6x + 8.
   
   
   1. What are the x-intercepts for the graph? Answer
    
   2. How many x-intercepts are there? Answer

6. The function from question 5 cannot be written in factored form. The partially factored form of this function is f(x) = 2(x2 + 3x + 4).
   
   
   1. Why can’t the function be written in fully factored form? Answer
    
   2. Can values for r and s be found? Answer
    
   3. What is the y-intercept of the graph? Answer
    
   4. If you didn’t have the graph, which form of the function can you use to find the y-intercept? Answer