Have a question Graph  y= (x - alpha) (x - beta) i) y = (x-1)(x+3) ii) y = (x+2 ) (x - 1) iii) y= (x+4) (x+2) iv) y= x (x-3) then find x intercepts which I have i) The x-intercept is -3 and 1 ii)...

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Graph

 y= (x - alpha) (x - beta)

i) y = (x-1)(x+3)

ii) y = (x+2 ) (x - 1)

iii) y= (x+4) (x+2)

iv) y= x (x-3)

then find x intercepts

which I have

i) The x-intercept is -3 and 1

ii) The x-intercept is -2 and 1

iii) The x-intercept is -4 and -2

iv) The x-intercept is 0 and 3

I now need to 

Comment on the significance of alpha and beta in 

y= (x - alpha) (x - beta)

I don’t see any significance or don’t understand what Im looking for.

Can anyone help…? please.

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Top Answer

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tiburtius | High School Teacher | (Level 2) Educator

Posted on

There are all four of your graphs i) red, ii) green, iii) blue and iv) purple.

Alpha and beta are actually x-intercepts (this is clearly visible from the graph). This can also be shown algebraically. if we put `x=alpha` we get

`y=(alpha-alpha)(alpha-beta)=0(alpha-beta)=0`

The case when `x=beta` can be shown analogously.

More generally this applies to all polynomials not only to quadratic function.

On the image below you can see graph of `y=(x-alpha)(x-beta).`    

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