SOLUTION: I need help finding the vertex of the parabola: y= -6.25x²+ 150x + 7200? I have graphed it and found the vertex to be (12, 8100) but I need to be able to find it algebraically.

Algebra ->  Sequences-and-series -> SOLUTION: I need help finding the vertex of the parabola: y= -6.25x²+ 150x + 7200? I have graphed it and found the vertex to be (12, 8100) but I need to be able to find it algebraically.       Log On


   

Question 604590: I need help finding the vertex of the parabola: y= -6.25x²+ 150x + 7200?
I have graphed it and found the vertex to be (12, 8100) but I need to be able to find it algebraically. I tried taking the derivative but I'm not sure I was doing that right or if thats how I should approach it. Please explain your steps, so that i can learn what and why you are doing what you do. Thanks in advance for all the help.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
y= -6.25x²+ 150x + 7200
.
The x-value of the vertex is at:
x = -b/(2a) (from the "quadratic formula" w/o the radical)
x = -150/(2(-6.25)
x = -150/(-12.5)
x = 150/12.5
x = 12
.
To find the y-value, plug the above back into the equation:
y= -6.25x²+ 150x + 7200
y= -6.25(12)²+ 150(12) + 7200
y= 8100