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.