(c) Find its maximum or minimum value. f(x) =

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A quadratic function is given.
f(x) = 8x2 − 16x + 1
(a) Express the quadratic function in standard form.
f(x) =

(c) Find its maximum or minimum value. 

f(x) = 
 
Jul 6th, 2015

Thank you for the opportunity to help you with your question!

The given equation is 8 x^2-16x+1

 Here a= 8, b= -16 and c= 1

Using the formula

x= -{b+-(b^2-4ac)}/2a Put the values of a,b and c. 

We get x1= 1+1/4 sqrt 14

x2= 1-1/4 sqrt 14

To find the maximum and minimum value, we will use Perfect square method.

Make the coefficient of x%5E2 positive by multiplying it by -1 in casea%3C0.
Maxima / Minima is decided from the sign of 'a'. 
If 'a' is positive then we have Minima and for 'a'negative we have Maxima.

Step two:
Now make the perfect square with the same x%5E2 and x coefficient. 
%282.82842712474619%2Ax+%2B+%28-16%2F2%29%29%5E2

Maxima / Minima lies at the point where this squared term is equal to zero.

Hence,
=>x=%28-%28-16%2F2%29%2F2.82842712474619%29=+2.82842712474619

This point is a minima if value of coefficient of x2 is positive and vice versa. For our function the point x=1 is a minima.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 6th, 2015

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