SOLUTION: for what value(s) of k will the graph of y = x^2-3x+k a) touch the x-axis b) never meet the x-axis?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: for what value(s) of k will the graph of y = x^2-3x+k a) touch the x-axis b) never meet the x-axis?      Log On


   

Question 155245: for what value(s) of k will the graph of y = x^2-3x+k
a) touch the x-axis
b) never meet the x-axis?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

It will touch the x-axis when the polynomial has only one solution. If the polynomial has only one solution, then the discriminant is equal to zero.


D=b%5E2-4ac Start with the discriminant formula


0=%28-3%29%5E2-4%281%29%28k%29 Plug in D=0, a=1, b=-3 and c=k


0=9-4%281%29%28k%29 Square -3 to get 9


0=9-4k Multiply


-9=-4k Subtract 9 from both sides


9%2F4=k Divide both sides by -4


So when k=9%2F4, then the polynomial will have only one solution and will touch the x-axis.



b)

Follow the same procedure described above, but this time D%3C0.