SOLUTION: The graph of the quadratic function y = (3k - 1)(x^2) - 6x +1 where k € R, has a positive concavity and passes through the x-axis twice. Find the range of possible values for k

Algebra ->  Functions -> SOLUTION: The graph of the quadratic function y = (3k - 1)(x^2) - 6x +1 where k € R, has a positive concavity and passes through the x-axis twice. Find the range of possible values for k      Log On


   

Question 1193921: The graph of the quadratic function y = (3k - 1)(x^2) - 6x +1 where k € R, has a positive concavity and passes through the x-axis twice. Find the range of possible values for k.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+%283k-1%29+x%5E2+-+6+x+%2B+1

has positive concavity when its graph, a parabola, opens upward, 
which is when the coefficient of x2 is positive, which means 
greater than 0, so solve the inequality for k:

3k-1%3E0

Also to pass through the x-axis twice, its discriminant must 
be positive to give it two unique real zeros.  So simplify 
and solve this inequality for k:

b%5E2-4ac%3E0
%28-6%29%5E2-4%283k-1%29%281%29%3E0

Now look at the two solutions to those two inequalities and 
fill in fractions in the two blanks. 

___ < k < ___

Edwin