A quadratic equation - Math Central

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Question from corinanna, a student:

Hi,
How do you find a quadratic equation given the domain & range,
& or the y-intercept?

Hi,

There is not enough information to completely determine the quadratic equation. For example I looked at $y = x^2 - 4x$ and $y = 16 x^2 - 16 x.$ For each of them the domain is the real line, the range is all $y \ge -2$ and they each have $y = 0$ as the y-intercept.

I plotted them below.

graphs

Penny

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