Comment on Scheitelpunkform by hippo2
If you like, I can show you how to transform a normal function of 2nd degree into the "Scheitelpunktsform."
I'll do it on the example of more simple function:
f(x)=2x²+4x-12
f(x)=2(x²+2x-6)
f(x)=2(x²+2x+1-1-6)
Here I add 1 and take it away again so I can form a binomial.
f(x)=2[(x²+1)-7]
f(x)=2(x²+1)-14
Here we have the "Scheitelpunktsform"
The minimum of the graph is at (-1/-14)
The "Scheitelpunktsform" can also be used to solve an optimation problem, if it uses a function of second degree. The problem with the cage in my other deviation can be solved that way.
I'll do it on the example of more simple function:
f(x)=2x²+4x-12
f(x)=2(x²+2x-6)
f(x)=2(x²+2x+1-1-6)
Here I add 1 and take it away again so I can form a binomial.
f(x)=2[(x²+1)-7]
f(x)=2(x²+1)-14
Here we have the "Scheitelpunktsform"
The minimum of the graph is at (-1/-14)
The "Scheitelpunktsform" can also be used to solve an optimation problem, if it uses a function of second degree. The problem with the cage in my other deviation can be solved that way.
Oh! We call this 'vertex' form! I haven't thought about it in so long...
We call it that because the 'vertex' is the maximum or minimum of the parabola, which is what makes this form special.
We call it that because the 'vertex' is the maximum or minimum of the parabola, which is what makes this form special.
I see. "Scheitelpunkt" is the german translation for "Vertex". Thank you for the explanation.
Thank you! This is very interesting.