2007 iTest Problems/Problem 51
Problem
Find the highest point (largest possible 
-coordinate) on the parabola
![\[y=-2x^2+ 28x+ 418\]](http://latex.artofproblemsolving.com/7/9/f/79fda67b1f2e64588c88901a47c2a1543516d336.png)
Solution
One way to find the highest point is to rewrite the quadratic into vertex form.
![\[y = -2(x^2 - 14x - 209)\]](http://latex.artofproblemsolving.com/6/f/6/6f6b554c46e022add26fe314731226f5391bd881.png)
Complete the square inside the parentheses.
![\[y = -2(x^2 - 14x + 49 - 49 - 209)\]](http://latex.artofproblemsolving.com/7/8/8/78875cf0e3d1c63d9ae90e1eb994d21cc23b0d88.png)
![\[y = -2((x-7)^2 - 258)\]](http://latex.artofproblemsolving.com/c/5/9/c596122765dacf49d6bf3b7bfb4936c4bab71637.png)
![\[y = -2(x-7)^2 + 516\]](http://latex.artofproblemsolving.com/5/d/2/5d2dfe590f7ebd175b086e16a8f4d58389951337.png)
Thus, the largest possible y-coordinate is 
.
See Also
| 2007 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 50 |
Followed by: Problem 52 | |
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