1955 AHSME Problems/Problem 39
Solution
The least possible value of 
is given at the coordinate of the vertex. The 
- coordinate is given by
![\[\frac{-p}{2}\]](http://latex.artofproblemsolving.com/7/c/9/7c99e20f2c679f85c800b622be00bb81be6a184c.png)
. Plugging this into the quadratic, we get
![\[y = \frac{p^2}{4} - \frac{p^2}{2} + q\]](http://latex.artofproblemsolving.com/6/a/2/6a2afa567a387b10458f22e8fc82be8049ae82f9.png)
![\[0 = \frac{p^2}{4} - \frac{2p^2}{4} + q\]](http://latex.artofproblemsolving.com/a/7/5/a759167c387574d4a12f3635947c8284350ca532.png)
$$ (Error compiling LaTeX. Unknown error_msg)0 = \frac{-p^2}{4} + q$
![\[q = \frac{p^2}{4} = \boxed{B}\]](http://latex.artofproblemsolving.com/3/5/4/354bd18bcb66eab365a35361dd29404c5dccc2ed.png)
~JustinLee2017
