Given:
#y=9x^2-27x+20# is a quadratic equation in standard form:
#y=ax^2+bx+c#,
where:
#a=9#, #b=027#, #c=20#
The formula for the axis of symmetry is:
#x=(-b)/(2a)#
#x=(-(-27))/(2*9)#
#x=27/18#
Reduce by dividing the numerator and denominator by #9#.
#x=(27-:9)/(18-:9)#
#x=3/2#
The axis of symmetry is #x=3/2#. This is also the x-coordinate of the vertex.
To find the y-coordinate of the vertex, substitute #3/2# for #x# in the equation and solve for #y#.
#y=9(3/2)^2-27(3/2)+20#
#y=9(9/4)-81/2+20#
#y=81/4-81/2+20#
The least common denominator is #4#. Multiply #81/2# by #2/2# and #20# by #4/4# to get equivalent fractions with #4# as the denominator. Since #n/n=1#, the numbers will change but the value of the fractions will remain the same.
#y=81/4-(81/2xx2/2)+(20xx4/4)#
#y=81/4-162/4+80/4#
#y=(81-162+80)/4#
#y=-1/4#
The vertex is #(3/2,-1/4)#.
graph{y=9x^2-27x+20 [-10, 10, -5, 5]}
