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.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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...

See
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Get 48 Hours Free Access

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

Approved by eNotes Editorial Team