Parts of Quadratic Curve Above or Below the X axis

Author:
Lew W.S.
You can change the function by entering in the input box or by dragging the curve . The left and right limits of the graph plotted can also be adjusted by just dragging the green arrowheads. Drag point P to find pairs of values of x and corresponding y values of the function.

What are the values of y on the part of the curve that is (a) below the x axis? (b) above the x axis ? (c) on the x axis ?

Can you describe with reference to points A and B (eg, left or right of A, between A and B etc) which part of the curve is (a) has negative values of y (ie. below the x axis)? (b) has negative values of y (ie. above the x axis)? (c) has value of y = 0 (ie. on the x axis) ?

Is it possible for all values x, that the value of y can be either (a) always positive or (b) always negative (Describe the shape of the curve for each case (a) and (b)