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Let $c$ be a real number.  What is the maximum value of $c$ such that the graph of the parabola $y = 2x^2$ has at most one point of intersection with the line $y = x+c?$

 Dec 20, 2023
 #1
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y = 2x^2

 

y = x + c

 

Set the functions equal 

 

2x^2   = x + c

 

2x^2 - x -  c =  0

 

To find one  point  of intersection set the discriminant  = 0  and solve for  c

 

(1)^2  - 4(2)(-c)  = 0

 

1 + 8c =  0

 

1 = -8c

 

c = - 1/8

 

cool cool cool

 Dec 21, 2023

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