Question 786276: Hi there tutors, I have a question that I don't know how to do. This is the equation : 5(x-3)^2+8.
I have to find:
1. The maximum or minium point.
2. The equation of the line of symmetry or the equation of the axis of symmetry.
3. The value of x at which the maximum or minimum of the axis of symmetry.
4. The x co-ordinate of the minimum or maximum point.
5. The range of the function
6. The maximum or minimum value.
7. The y co-ordinate of the maximum or minimum point.
Sorry if it seems like to much and thanks to whomsoever in advance.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 1) The function  or 
takes the value  when  <---> 
For all other values of  ,
 ,  ,  , and 
So the point (3,8) (with and is a minimum, because the function's value is greater everywhere else, and it takes the value y=8 only for x=3.
2) In the function appears only in  , and
 is the horizontal distance to the vertical line .
The value of determines the value of  , so that any two points on opposite sides, but at the same horizontal distance from have the same . If the line were a mirror, the points of the graph on one side would be the mirror image of the points on the other side.
is the equation of the "line of symmetry" or "axis of symmetry."
3) I do not know what you meant by "The value of x at which the maximum or minimum of the axis of symmetry."
4) The x co-ordinate of the minimum or maximum point is as explained in 1).
5. The range of the function is [8,infinity) can get as large as you want. There are no bounds for , except tha it must be  . It cannot be less than 8, but it can be more than any number you can name.
6. The maximum or minimum value. As said for 1) the minimum value for y is 8.
7. The y co-ordinate of the maximum or minimum point. y=8, as said before.
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