2007 iTest Problems/Problem 51

Problem

Find the highest point (largest possible $y$-coordinate) on the parabola \[y=-2x^2+ 28x+ 418\]

Solution

One way to find the highest point is to rewrite the quadratic into vertex form. \[y = -2(x^2 - 14x - 209)\] Complete the square inside the parentheses. \[y = -2(x^2 - 14x + 49 - 49 - 209)\] \[y = -2((x-7)^2 - 258)\] \[y = -2(x-7)^2 + 516\] Thus, the largest possible y-coordinate is $\boxed{516}$.

See Also

2007 iTest (Problems)
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
Invalid username
Login to AoPS