The maximum or minimum point (vertex) of the graph of 



has x-coordinate = 

If a is a positive number, the vertex is a minimum.
If a is a negative number, the vertex is a maximum 

Its y-coordinate is found by substituting the value of the x
coordinate for x into 

It's zeros are 

,0) 

and

,0)

The axis of symmetry is the vertical line which passes through the 
vertex and has the equation



The y-intercept is (0,c)

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Identify the maximum or minimum (vertex), zeros, and axis of symmetry line and show the graph.

y=x^2-4x+1

a=1, b=-4, c=1


The maximum or minimum point (vertex) of the graph of 





a=1, b=-4, c=1

has x-coordinate = 

                 = 
  
                 = 

                 = 

a=1 is a positive number, so the vertex is a minimum.

Its y-coordinate is found by substituting the value of the x
coordinate for x into 

Substituting 2 for x






So the y-coordinate is -3 and so the vertex has
coordinates:

(2, -3)

It's zeros are 


(,0) 

and

(,0)

Substituting  a=1, b=-4, c=1


(,0)

(,0)

(,0)

(,0)

(,0)

(,0)

(,0)

(,0)

Similarly just be changing the sign before the radical term
above, the other zero is

(,0)

They are approximately (.27,0) and (3.73,0)

The axis of symmetry is the vertical line which passes through the 
vertex and has the equation



which is



We plot the vertex, the x-intercepts and the axis of symmetry (in green).
and the y-intercept is (0,c)



Then sketch in the graph:




Edwin