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\(\text{Find all numbers $a$ for which the graph of $y=x^2+a$ and the graph of $y=ax$ intersect. Express your answer in interval notation. }\)

 Dec 31, 2019
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y = x^2  +  a

y = ax

 

Setting the y's equal 

 

x^2 + a   = ax       rearrange as

 

x^2  - ax  +  a   = 0

 

For us to have real solutions.....the  discriminant must be ≥ 0

 

So

 

a^2  - 4a  ≥  0

 

a ( a - 4) ≥  0

 

This will  be true on these intervals

 

a ≥ 4       and      a ≤ 0

 

So

 

(-infinity , 0 ]   U   [4, infinity )

 

 

cool cool cool

 Dec 31, 2019

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