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.
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
sorry the rest of the problems
Given the following function, find:
(a) vertex, (b) axis of symmetry, (c) intercepts, (d) domain, (e) range,
(f) intervals where the function is increasing,
(g) intervals where the function is decreasing, and
(h) the graph of the function Please show all of your work.
f(x) = -x^2+4x