SOLUTION: determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.
f(x) = 2x^2+12X
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Question 464898: determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.
f(x) = 2x^2+12X
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Your first difficulty is that your 
is NOT a quadratic function. A quadratic function has the form:
\ =\ ax^2\ +\ bx\ +\ c)
Where 
AND the variable in the first and second terms are the same. 
and 
are NOT the same thing. However, I'm going to proceed on the presumption that you meant them to be the same thing.
Under the presumptive conditions, you have a quadratic function of the form:
Where 
, 
, and 
The graph of such a function is a parabola. If 
then the parabola opens upwards and the vertex of the parabola is a minimum point, that minimum being the value of the function at the vertex. If 
then the parabola opens downward and the vertex represents a maximum.
To find the -coordinate of the vertex use the formula:
To find the 
-coordinate of the vertex, evaluate the function at 
\ =\ a\left(x_v\right)^2\ +\ b\left(x_v\right)\ +\ c\ =\ a\left(\frac{-b}{2a}\right)^2\ +\ b\left(\frac{-b}{2a}\right)\ +\ c)
John
My calculator said it, I believe it, that settles it
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