Question 677673: find the vertex of the parabola
F(x)=2x^2+8x+3
Can you please show the work so that I can get a full understanding.
Thank you Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
This is a parabola with a minimum and not a maximum
I can tell because the squared term is positive. If I changed it
to then it would have a maximum.
The vertex is the (x,y) point at the minimum ( or maximum )
---------------
The x-coordinate of the vertex occurs halfway
between the roots, which are
the two solutions to
---------------
To get a deeper understanding of this look at the
quadratic formula which gives these two solutions
---------------
Now I'll separate the terms in each solution:
-----------------------------------------
Now what you have is: = ( x coordinate of the vertex ) + ( the positive correction ) = ( x coordinate of the vertex ) - ( the negative correction )
-------------------
So, you can see that is the x-coordinate of the vertex
when the form of the equation is
-------------------
I can apply this to your problem
--------------------
Now you know the vertex is at ( -2, y ). To find y, plug
into the equation
---------------
The vertex is at ( -2, -5 )
Here's a plot of the equation:
The vertex is where is should be
