Student worksheet
Quadratic modelling of the number of males registered in apprenticeship programs

1. In general, what does h represent?
   
   
   
2. Specific to this dataset, what does h represent?
   
   
   
3. By inspection of your scatter graph, what is a reasonable approximation of h?
   
   
   
4. In general, what does k represent?
   
   
   
5. Specific to this dataset, what does k represent?
   
   
   
6. By inspection of your scatter graph, what is a reasonable approximation of k?
   
   
   
7. What is the difference in the parabola between a quadratic equation with a positive a value and a quadratic equation with a negative a value?
   
   
   
8. What happens if a is zero? Discuss in terms of both the equation and the resulting graph.
   
   
   
9. If a quadratic equation has a positive a value, will the vertex of the parabola be a maximum or a minimum? Why?
   
   
   
10. If a quadratic equation has a negative a value, will the vertex of the parabola be a maximum or a minimum? Why?
    
    
    
11. How does changing the value of a affect the shape of a parabola?
    
    
    
    
    

    *****Return to your instruction sheet and complete the final step before answering questions #12 to 18 *****

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12. What is your best value for a?
    
    
    
13. What is your best value for h?
    
    
    
14. What is your best value for k?
    
    
    
15. Write your equation here in the form y = a(x - h)² + k.
    
    
    
16. How are h and k related?
    
    
    
17. What is the vertex of your graph? What does this mean in terms of this dataset?
    
    
    
18. Paste your graph here.