Determine the coordinates of the vertex of the function f = 2x^2-5x+3.

f(x) = y = 2x^2-5x+3. to find the
vertex.

Solution:

y =
2x^2-5x+3

y/2 = x^2
-5x/2+3/2

y/2 = (x-5/4)^2 -
(5/4)^2+3

y/2 = (x-5/4)^2  + (-25+48)/1= (x-5/4)^2 +
(23/16)

y/2 -23/16) =
(x-5/4)^2

(1/2) (y-23/8) = (x-5/4)^2. If we compare this
parabola with the standard parabola  4aY =  X^2 with vertex X = 0 and Y = 0, we
get

x-5/4 = 0 and y-23/8 = 0 gives the coordinates of the
given parabola.

So x= 5/4 and y = 23/8 are the coordinates
of the vertex.