For the function y = -x^2 + 4x,  find the vertex, axis of symmetry, intercepts, domain, range, and the graph of the function. Also, where is the function increasing and decreasing.

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The function we have is y = -x^2 + 4x

The graph of y = -x^2 + 4x is:

The vertex of the function is (2, 4). The axis of symmetry is x = 2, The x- intercepts are (0,0) and (4, 0). The y-intercept is (0,0), The domain of the function is all real values of x. The range of the function is (-inf., 4)

To find where the function is decreasing and increasing we need f'(x) = -2x + 4

It is increasing when -2x + 4 > 0 or x < 2. It is decreasing when -2x + 4 < 0 or 2x > 4 or x > 2

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