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suppose that f(x) and g(x) are both quadratic functions with graphs that open down. explain how you know what type of function y = f(x) + g(x) must be. in which direction does the graph open? where is the maximum point of this function in relation to the maximum points for the first two functions? explain your answers.

 Apr 29, 2019
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f(x) + g(x)  will also be quadratic functions opening dowward.....we cannot make any general statement about the max of the new function formed

 

For example  if  f(x) = -2x^2, g(x)  = -3x^2  then f(x) + g(x)  = -5x^2

And all of these have the same max at the origin

 

But  f(x) = -2x^2 + 3  and  g(x) = -3x^2 + 5    have maxes at (0, 3) and (0, 5), respectively

 

But f(x) + g(x)  =  -5x^2 + 8  has a max at (0, 8)

 

 

cool cool cool

 Apr 29, 2019

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