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ritwik06
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SOLVED
While going through a question, I came across a function [tex]f(x)=5^{x}+5^{-x}[/tex]
I saw its graph through a software. It was a parabola with minimum value 2.
Now a question arises in my mind.
Every function of the type [tex]g(x)=ax^{2}+bx+c[/tex] is a parabola.
Can I assume the corollary to be true, that is for every parabola, there exists a quadratic function??
If yes, how may I find the coefficients a,b,c such that f(x)=g(x) ?
There is only one thing that I see-
[tex]\frac{-\Delta}{4a}=2[/tex]
Can this be solved?
Homework Statement
While going through a question, I came across a function [tex]f(x)=5^{x}+5^{-x}[/tex]
I saw its graph through a software. It was a parabola with minimum value 2.
Now a question arises in my mind.
Every function of the type [tex]g(x)=ax^{2}+bx+c[/tex] is a parabola.
Can I assume the corollary to be true, that is for every parabola, there exists a quadratic function??
If yes, how may I find the coefficients a,b,c such that f(x)=g(x) ?
The Attempt at a Solution
There is only one thing that I see-
[tex]\frac{-\Delta}{4a}=2[/tex]
Can this be solved?
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