SAT Math: Find the Maximum Value of f(x) = -2(x - 5)² + 18 in Under 5 Seconds
In vertex form f(x) = a(x - h)^2 + k, since a = -2 < 0, the parabola opens downward and the vertex (5, 18) is the absolute maximum point. The maximum value of f(x) is 18 (occurring at x = 5).
Exact Question Text
What is the maximum value of the function $f(x) = -2(x - 5)^2 + 18$?
Step-by-Step Solution
- In $f(x) = a(x - h)^2 + k$:
- Vertex is $(h, k) = (5, 18)$.
- Since $a = -2 < 0$, the vertex is a maximum.
- The maximum value of the function is $18$ (at $x = 5$).
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