Answer:
- f(x) — maximum at (-4, 2)
- g(x) — minimum at (2, -2)
Step-by-step explanation:
You want to identify whether the vertex of the given parabolic functions is a minimum or a maximum.
Vertex form
The vertex form of a quadratic function is ...
f(x) = a(x -h)² +k
This function has its vertex at (h, k). The vertical scale factor is 'a'.
When a > 0, the graph opens upward, and the vertex is a minimum.
When a < 0, the graph opens downward, and the vertex is a maximum.
Application
Here, we have ...
- for f(x): a = -1, (h, k) = (-4, 2). The vertex is a maximum.
- for g(x): a = 1, (h, k) = (2, -2). The vertex is a minimum.
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Additional comment
The "work" is to inspect the equation to determine the sign of the leading coefficient, 'a'.
