Thread: find values for x

Hi, I have a problem that trying to solve all evning and it is in two parts (a) If is a positive constant, find the set of valus of for which is negative. Find the value of a if this function has a minimum value of -27.
(b) Find two quadratic funcions of which are zero at , which take the value of 10 when and which have a maximum value of 18. Sketch the graps of these two functions. Can ou help me with this problem?

Originally Posted by scrible

If is a positive constant, find the set of valus of for which is negative. Find the value of a if this function has a minimum value of -27.

If a is positive then we need to find where . Start by finding out where the trinomial is zero. I get these to be at x = -4 and x = 2. It is simple to see that the negative range for this is -4 < x < 2.

Can you get the rest from here? (Hint: Consider where the parabola has its absolute minimum.

-Dan

Originally Posted by scrible

(b) Find two quadratic funcions of which are zero at , which take the value of 10 when and which have a maximum value of 18. Sketch the graps of these two functions.

You are speaking of a quadratic. The general form is


For x = 1 we have a zero, so y = 0.


When x = 0 we have y = 10, so


So far the quadratic is

where

Now, we know that the quadratic has a maximum of 18. This means that a is negative. The last step is a bit involved, but if you recall,

You can plug that into the equation to get

(Recall that the maximum y is 18.) It's tedious but you will get a quadratic in a that give you your two solutions.

-Dan