Expert: Richard J. Raridon - 10/19/2009

Question
Hello,
I've tried to sketch a curve but it doesn't seem to come quite right, but I'm sure all my calculations are correct. Could you tell me where I'm wrong please?
By completing the square, sketch the curve Y=1+3x-2xsqared
(the last x is squared)
so I've found the y-intercept by making x=0:
y=1+3.0-2.0
y=1

then i've found the maximum value and axis of symmetry:
y=1+3x-2xsquared
y=-2(xsquared-3/2x)+1
y=-2[(x-3/4)sqared -9/16]+1
y=-2(x-3/4)squared +9/8 +1
y=-2(x-3/4)squared +17/8
so the axis of symmetry is 3/4 and the maximum value is 17/8

after this i found the x-intercepts which gives me
x=+2.8 and x=-1.3
if you sketch the graph you'll notice the parabola doesn't go through the y-intercept.


Answer
I don't know exactly what you did but you didn't get the x-intercepts right.  You get them by setting y = 0 and solving for x to get x = 1.78, -0.28
Obviously, you didn't sketch it correctly since it has to go through the y-intercept.  
By differentiating, I get a max. value of 3/4, not 17/8