SOLUTION: Calculate the range of values of c for which 3x^2-9x+c>2.25 for all values of x. Explain clearly why the graph must be above the x axis?

Algebra ->  Graphs -> SOLUTION: Calculate the range of values of c for which 3x^2-9x+c>2.25 for all values of x. Explain clearly why the graph must be above the x axis?      Log On


   

Question 967191: Calculate the range of values of c for which 3x^2-9x+c>2.25 for all values of x.
Explain clearly why the graph must be above the x axis?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The graph is either entirely above or entirely below the x-axis. Seeing that the coefficient of the leading term is a POSITIVE 3, the graph has a vertex at the minimum and opens upward. This logically means that the graph is above the x-axis everywhere. (As long as the correct value is found for c).

You want the discriminant to be less than 0 for 3x%5E2-9x%2Bc-2.25%3E0.
That means %28-9%29%5E2-4%2A3%2A%28c-2.25%29%3C0. Find the solution inequality for c.