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, Answer Key)
Preceded by:
Problem 50
Followed by:
Problem 52
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