Difference between revisions of "2007 iTest Problems/Problem 51"
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Rockmanex3 (talk | contribs) (Solution to Problem 51 - easy!) |
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== Solution == | == Solution == | ||
| + | |||
| + | One way to find the highest point is to rewrite the quadratic into vertex form. | ||
| + | <cmath>y = -2(x^2 - 14x - 209)</cmath> | ||
| + | Complete the square inside the parentheses. | ||
| + | <cmath>y = -2(x^2 - 14x + 49 - 49 - 209)</cmath> | ||
| + | <cmath>y = -2((x-7)^2 - 258)</cmath> | ||
| + | <cmath>y = -2(x-7)^2 + 516</cmath> | ||
| + | Thus, the largest possible y-coordinate is <math>\boxed{516}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{iTest box|year=2007|num-b=50|num-a=52}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 18:59, 16 June 2018
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
