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Answer:
Vertex: (-1, 4)
Maximum: f(-1) = 4
Increasing: (-∞, -1)
Decreasing: (-1, ∞)
Explanation:
The equation can be written in vertex form by "completing the square."
First factor out the leading coefficient from the x-terms.
f(x) = -(x² +2x) +3
Then add the square of half the x-coefficient inside parentheses. Add the opposite of that amount outside parentheses.
f(x) = -(x² +2x +1) +3 +1
Write in vertex form.
f(x) = -(x +1)² +4 . . . . . . . compare to a(x -h)² +k
You can see that the vertex is (h, k) = (-1, 4), and that the vertical scale factor 'a' is negative. This means the vertex is the maximum and the parabola opens downward.
The function will be increasing to the left of the maximum, decreasing to its right.
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Vertex: (-1, 4)
Maximum: f(-1) = 4
Increasing: (-∞, -1)
Decreasing: (-1, ∞)
Graph: see attached