help ! how do you find the vertex of a problem graphically?

Answer 1

One way is to differentiate:-
Example
f (x) = 3 x ² + 2
f `(x) = 6 x = 0 for turning point
x = 0 for turning point
f "(x) = 6 is +ve so turning point is a MINIMUM turning point.
f(0) = 2
Turning point is (0 , 2) and this is a minimum turning point.

Hope this example helps.

Answer 2

Depends on what type of graphing calculator you have. Personally, I have a Texas Instruments, so I will explain that way.

You will need to enter the function, under "Y=". Graph the function.

Then you will need to go to "CALC" (You will need to hit the "2nd" (yellow button first).

Then, select either "minimum" or "maximum". Since the vertex of a parabola occurs at the "hill top" or "valley bottom", you will need to either choose minimum or maximum depending on the shape of the graph.

Once you have selected the "min" or "max", you will be asked to enter a "Left Bound" and "Right Bound", and then a "Guess". For a left bound, enter an x-value that is to the left of the vertex, same for the right bound, enter a x-value to the right of the vertex. For the guess, choose what you might think it is, then the calculator will give the "X =" and "Y = " coordinates of the vertex.

Vertex: (X,Y)