#2y=10x^2+7x-3#
Divide by 2:
#y=5x^2+7/2x-3/2#
We now have the form:
#color(red)(y=ax^2+bx+c)#
We need the form:
#color(red)(y=a(x-h)^2+k)#
Where:
#bba color(white)(8888)# is the coefficient of #x^2#
#bbh color(white)(8888)# is the axis of symmetry.
#bbk color(white)(8888)# is the maximum or minimum value of the function.
It can be shown that:
#h=-b/(2a)color(white)(8888)# and # color(white)(8888)k=f(h)#
#:.#
#h=-(7/2)/(2(5))=-7/20#
#k=f(h)=5(-7/20)^2+7/2(-7/20)-3/2#
# color(white)(8888)=245/400-49/40-3/2#
# color(white)(8888)= 49/80-49/40-3/2#
# color(white)(8888) =(49-98-120)/80=-169/80#
Vertex form:
#y=5(x+7/20)^2-169/80#
