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Here is what I have to do:

Answer the question in the way that the question directs you to answer it. For instance, if a question asks you to complete the square to solve for the vertex (using vertex form), you should not use the method for finding the vertex from the standard form of the equation to earn your points. 


Consider the function:

(This is an example problem, I am having trouble solving it, I need to explain how to get the answer as if the answers were not there.) Please help, I'd really appreciate it!

 Mar 22, 2018

This is a parabola.....In this form.....when the coefficient in  front of x is negative


y  = -ax^2  + bx  + c.....we have a parabola that opens downward  with the vertex the highest point on the graph


So......we have


y  = (-1)x^2  +  (-2)x  + 8


The  x coordinate of the vertex  is given by   -b/ [ 2a]

So  b = -2     and  a  = -1


So....the x coordinate of the vertex  =    - (-2) / [2 (-1)]  = 2/-2  = -1


Since this is the highest point on the graph of this parabola....the function will increase  on this interval :    (-inf, -1 )


However we must find out where the parabola is positive......we can  find the x intercepts by letting y  =0  and solving for x....so we have


0  = -x^2 -2x + 8        multiply through by  -1


0  =x^2 + 2x  - 8        factor


0 = (x - 2) ( x + 4)


Setting each factor to 0  and solving for x  produces the x intercepts of  x  = 2  and x  = -4


So......the graph will  be positive  and increasing from    -4 < x < -1  


See the graph here to get a feel for this :





cool cool cool

 Mar 22, 2018

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