Question 841179: I am having trouble understanding how to solve the following question. My textbook does not explain each in detail.
Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, (d) range. Then determine (e) the interval of the domain for which the function is increasing and (f) the interval for which the function is decreasing.
f(x)=-3(x-2)^2+1
If someone can explain how to actually arive at each, then I will understand how to solve similar problems. I guess my textbook is expecting me to already know how to, which kind of defeats the purpose of taking a class to learn.
Thanks in advance!
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! In general, the vertex of the function f(x) = a(x-b)^2 + c is the point (b,c) (this is fairly easy to check) so the vertex of f(x) is at (2,1). The axis of symmetry is the vertical line x = 2. The domain of any polynomial function in a real variable is assumed to be the set of all real numbers. To look at the range, note that f(x) is a downward pointing parabola. Therefore it attains its maximum at the vertex (2,1) so max(f(x) = 1. The range is (-infinity, 1].
The parabola is increasing on (-infinity, 2) and decreasing on (2, infinity) (since x = 2 is the x-coordinate of the vertex). You may want to graph the polynomial on Wolfram Alpha or your calculator.
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