Question
Determine the vertex of the graph of the following parabola. \[ f(x)=-3(x-3)^{2}-2 \]
Ask by Estrada Fleming. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The vertex of the parabola is (3, -2).
Solution
The given quadratic function is already in vertex form, which is:
f(x) = a(x - h)² + k
Comparing f(x) = -3(x - 3)² - 2 with the vertex form, we identify:
h = 3
k = -2
Therefore, the vertex of the parabola is (3, -2).
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Simplify this solution The Deep Dive
The vertex of a parabola in the form \( f(x) = a(x-h)^2 + k \) is given by the point \( (h, k) \). In your equation, \( f(x) = -3(x-3)^2 - 2 \), we can identify \( h = 3 \) and \( k = -2 \). Therefore, the vertex of the graph is at the point \( (3, -2) \). Additionally, since the coefficient \( a = -3 \) is negative, the parabola opens downward, suggesting a maximum value at the vertex. This can be helpful when analyzing the function’s behavior, as it indicates that the vertex represents the highest point on the graph.
