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Quadratic Relations in a form of : y=a(x-r)(x-s) 

 

Quadratics relations of the form of y = a (x-r) (x-s) help you determine the x- intercepts/zeroes/ roots. 

 

In factor form: y= a (x-r) (x-s) the two x- intercepts to be determined are the r  and s in the equation. 

 

Example: y= (x+2) (x-4)

 

Let each bracket equal to 0

 

x+2=0                      x-4=0 

x = -2                       x=4 

 

 

 

 We have our two intercepts. 

 

 

 

Axis of Symmetry

After find the two x- intercepts. You have to find the axis of symmetry, also the x co-ordinate in your vertex.

 

Formula to find the axis of symmetry (AOS) is: [ (x+r) /2]

 

AOS=  (-2) + (4)

                2

 

AOS= 2

           2

 

AOS= 1

 

 The axis of symmetry is 1 also the x- co-ordinate in the vertex is 1. 

 

 

Optimal Value

 To find the optimal value or so called the y- intercept and also the y- co-ordinate in the vertex. 

You would sub in the AOS  in the equations and solve for y.

 y= (x+2) (x-4)

 y= (1+2)(1-4)

 y= (3) (-3)

 y= -9

 

y- intercept: (0,-9)

 

Your vertex is at ( 1, -9)

 

To see another example: