# Investigating the general parabola

- Author:
- Cliff-Lee

**Investigating the general parabola**

By experimenting with the a,b,c parameters of the parabola comment on your findings to the below questions,
1. What do you notice about the value of b^2-4ac when the parabola has
i) Two roots
ii) One root
iii) Zero roots
With reference to the quadratic equation formula, explain why this makes sense.
2. What is the relationship between the two roots, and the axes of symmetry?
How far is each root from the axes of symmetry?
Which parameters affect the axes of symmetry and which do not?
Given two roots would you be able to state the axes of symmetry without reference to the
equation of the parabola?
3. As you alter the a parameter, how does this affect the vertex of the parabola? Could you generate an equation to describe the locus of the vertex.
4. As you alter the b parameter, how does this affect the vertex of the parabola? Could you generate an equation to describe the locus of the vertex.
5. As you alter the c parameter, how does this affect the vertex of the parabola? Could you generate an equation to describe the locus of the vertex.