Hello, mibamars!
Here's the first one . . .
For the parabola whose range is ,
whose xcoordinate of the turning point is 4,
and whose yintercept is
Find:
(1) the ycoordinate of the turning point.
(2) the equation of the parabola
(3) the coordinates of the xintercepts.
The general equation of a parabola is: .
Make a sketch . . . Code:

(4,3) 
* 
* * 
* * 
* * 
        +     
* *


* *

Since is on the parabola: .
The equation (so far) is: .
Since the range (values of y) is < 3,
. . and the xcoordinate of the turning point is 4,
. . clearly the vertex is (4,3).
The xcoordinate of the vertex is given by: .
. . So we have: . . [1]
Since (4,3) is on the parabola: .
. . which simplifies to: . . [2]
Subtract [2] from [1]: .
Substitute into [1]: .
For the xintercepts: .
Multiply by 3: .
. . Factor:.