# Vertex form of the function

Is it possible to solve and explain this question in a different way? I am working on an online mathematics Helper web site and I need solutions in different ways. This is not a homework or any kind of exam as I already have a solution of these questions. I just need different ways of solutions so that I can write different algorithms on those solutions and then call them in software coding randomly.

Math / ScienceMiscellaneous

Last Comment
mustish1
CompProbSolv

A very different approach (that may be much easier to program is:

Take the first derivative of the function
Solve it for 0 (i.e. what x gives you a first derivative =0?)
Plug that x in the original function to get the value of y
CompProbSolv

Depending on the form of the original function, this may be very straightforward.
CompProbSolv

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mustish1

Can you please show me a little bit work as I am not in touch with calculus since a long time.
I think first derivative of that equation would be:
2x-8+0
2x=8
x=4
The original function is:
x^2-8x+7=0
substituting x
8-32+7=0
y=31
I am not sure if this is correct. or I may mixing the integration with derivation.
CompProbSolv

x^2-8x+7=y is:
16-32+7=y
-9=y
mustish1

IS THIS IS CORRECT

Second derivative of the same equation:
x^2-8x+7=0

I think x=0

substituting x in that equation
y=7
CompProbSolv

The second derivative of x^2-8x+7 is the first derivative of the first derivative.

So... the first derivative is 2x-8

The second derivative is 2.

Since the second derivative is positive, then the point is a minimum.  That is, the function slopes upward on either side of that point.

Note that the second derivative doesn't depend on x.  That means that as you move from left to right on the graph, its slope increases.  When the slope is negative (as in to the left of the vertex), "slope increases" means it becomes less negative.
mustish1

Thank You.
Miscellaneous

A miscellany is defined as a "collection of various pieces of writing by different authors", but it has come to mean something "Of items gathered or considered together of various types or from different sources" or "a collection or group composed of members or elements of different kinds". The word "miscellaneous" comes from the Latin word "miscere", meaning "to mix." You might have heard the expression "a mixed bag," which applies when you don't quite know what you're going to get. More commonly, a miscellaneous group is made up of an odd group of things that don't fit anywhere else.

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