Question

What causes parabolas to expand and contract?

Answer 1

The coefficient of `x^2` affects expansion and contraction. See explanation.

Explanation:

In the graph `y=ax^2`, if `a > 1`, the curve looks more "squeezed" and if `0 < a < 1`, the curve looks more "expanded".

`y=x^2`
graph{x^2 [-10.17, 9.83, -1.04, 8.96]}
`y=5x^2`
graph{5x^2 [-10.25, 9.75, -0.48, 9.52]}
`y=1/5x^2`
graph{1/5x^2 [-10.29, 9.71, 0.08, 10.08]}

P.S. Sorry if this isn't the answer you were talking for.