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Question 539786: Given the following quadratic equation, determine if it has a maximum or a minimum value. Then find the maximum or minimum value.
f(x)=4x^2 + 2x - 9
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A quick look tells you that for x=0 y=-9, but far on either side of zero you have, for y=411 x=10 and y=371 for x=-10. Somewhere between x=-10 and x=1-=0 there is a minimum, and as you go to extreme positive and negative values for x, it increases to huge values. It's all the fault of that  term, which is going to be positive and grow without limits (much faster than the term in x).
Your teacher may tell you to memorize a rule that says that if the leading coefficient (that 4 right after the equal sign) is positive the quadratic curve has a minimum and a smiley face shape, and if the coefficient is negative, then it has a maximum and frowns. Do you really have to memorize that? Isn't it obvious if you think about it for a little while?
OK, let's find that maximum.
I am good at completing the square, so I know that
 , so
The minimum will happen when  <--> 
At that point  
Your textbook will tell you that a generic quadratic function 
will have a minimum or maximum at 
and that you can substitute that value in f(x) to find the y value at the maximum or minimum. They expect you to memorize .
Later they will expect you to memorize
 to find the zeros of the function.
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