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Find all numbers a for which the graph of y=x^2+a and the graph of y=ax intersect. Express your answer in interval notation.

 May 3, 2019
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y  = x^2 + a      y =ax

 

Set these equal  

 

x^2 + a  = ax

 

x^2 -ax + a  = 0

 

The discriminant   is

 

a^2 - 4a

 

To have real solutions.....this must be    ≥   to 0....so

 

a^2 - 4a    ≥  0

 

a ( a - 4)   ≥ 0  

 

This will be true for a on these intervals  :    (-inf, 0 ]  U [ 4, inf)

 

 

cool cool cool

 May 4, 2019

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