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]}