# Quadratic functions in Vertex Form

- Author:
- Dawn Roberts, Matthew Gill

- Topic:
- Functions, Quadratic Functions

Investigate the properties of a quadratic function of the form .

## Exploration: Record your answers on a separate sheet of paper or document.

NB:
1: Do you see a horizontal line? (If not, see above.) Why is the function initially a straight line? and adjust the value of . What happens to the function? and adjust the value of . Does anything appear to happen to the function? to be positive. How did the function change? Why is it not a straight line?
5: Adjust the value of to be negative. How did the function change compared to question 4?
6: Describe the effect that has on the function.
7: Ensure that is NOT equal to .
8: Adjust the value of . How does the function change?
9: Adjust the value of . How does the function change? Give two differences in the way the function changes compared to when you adjusted . and . How do they relate to the turning point?
11: Describe the effect that has on a quadratic function.
12: Describe the effect that has on a quadratic function.
13: Now set . Does the function change as you adjust . Give a reason for your answer.

**Start with****,****and***Hint: Look at the equation.*2: Leave*Reset.*3: Leave*Reset.*4: Adjust the value of*Reset, and ensure a is NOT equal to 0.*10: Identify the turning point of the function. Adjust the values of