Advent calendar 2022
10 December
A line is tangent to a curve if the line touches the curve at exactly one point.
The line \(y=-160\,000\) is tangent to the parabola \(y=x^2-ax\). What is \(a\)?
Show answer
Hide answer
A line \(y=\text{constant}\) that is tangent to a parabola must be a tangent to the minimum (or maximum) point.
\(y=x^2-ax\) can be rewritten as \(y=(x-a/2)^2-a^2/4\). The minimum of this will be at \(y=-a^2/4\).
If \(-a^2/4=-160\,000\), then \(a\) is 800.
