Step 1: Put the equation into factored form

 

y = x^2 - 8x + 15

y= (x-3)(x-5)

 

Step 2: Find the zeroes by setting each bracket equal to 0

 

x=3     x=5

 

Plot these x intercepts onto your graph

 

 

Step 3: Find the axis of symmetry (x value of the vertex)

x = 3+5

       2

x= 4

 

Step 4:  Find the optimal value (y value of the vertex)

 

y = x^2 - 8x + 15

y= (4)^2 - 8(4) + 15

y= -1

 

The vertex is (4,-1)

 

Step 5: Plot the vertex and connect the points