Please Help with Math. Will give 5 stars to whomever answers?

y = x^2 - 5x + 6

Factor:
y = (x - 6)(x + 1)
y = 0 when x = -1 or 6.

Therefore the axis of symmetry is between x = -1 and 6.
So the axis of symmetry is the line x = 5/2.

The vertex is the point on the curve and on the axis of symmetry so plug in 5/2 to the equation of the curve.

y = (5/2)^2 - 5(5/2) + 6
y = (25/4) - (25/2) + 6
y = -1/4

Answers:
Axis of Symmetry: x = 5/2
Vertex: (5/2, -1/4)

Look up the Common Core, coz my answer will likely get you a failing grade.

y = [ x² - 5x + 25/4 ] - 25/4 + 6
y = [ x - 5/2 ]² - 1/4
Vertex (5/2 , - 1/4)
Axis of symmetry is x = 5/2

if you convert the equation to vertex by completing the square

x^2 - 5x + 6 = y
x^2 - 5x + (5/2)^2 + 6 - (5/2)^2 = y
x^2 - 5x + 25/4 + 6 - 25/4 = y
(x - 5/2)^2 - 1/4 = y

y = (x - h)^2 + k

where h, k is the vertex

h = 5/2
k = -1/4

(5/2, -1/4) is the vertex

x = 5/2 is the axis of symmetry

Axis of symmetry: x=2.5

Vertex = (2.5,-.25)
Also written as (5/2, -1/4)

The vertex is found by taking the first derivative and determining the value of x for which y is a minimum.
The axis of symmetry is x=a where a is the value of x that minimises y.

Another approach without calculus is to factorise the quadratic to find the two roots. The value of a is the arithmetic mean of these two roots.