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?

Guest Oct 25, 2020

#1**+1 **

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

ElectricPavlov Oct 25, 2020