Thread: Semi-circle function

The graph of y=(3x-x)^.5 is a semi-circle with diameter coincident with the positive x-axis, radius 1.5, center at (1.5,0). create a function passing through (3.5,5) and intersecting the x-axis at x=2 and x=5.

Hello, sjenkins!

The graph of y=(3x-x)^.5 is a semi-circle with diameter coincident
with the positive x-axis, radius 1.5, center at (1.5,0).
. . All this is all true . . . but who needs it ??

Create a function passing through (3.5, 5) and intersecting the x-axis at x=2 and x=5.

Make a sketch . . .

Code:

        |
        |    (3½,5)
        |       *
        |
        |
        |
    - - + - * - - - * - -
        |   2       5

We can see that a parabola will work.

From the two x-intercepts, we have: .

To pass through , we have: .

. .


Therefore: .