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If the parabola y_1  =x^2 + 2x + 7 and the line y_2 = 7x + b intersect at only one point, what is the value of b?

 Oct 25, 2020
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Set the equations equal to find where they intersect:   ( I changed 'b' to 'n'  for clarity)

 

x^2 + 2x+7 = 7x+n

x^2 -5x + (7- n) = 0         for there to be only ONE point of intersection, the discrimnant = 0

b^2 - 4ac = 0

-5^2 - 4 (1)(7-n) = 0

25 -28 + 4n = 0

n = 3/4

 

Here is a graph:

https://www.desmos.com/calculator/boktuzssdd

 Oct 25, 2020

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