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?
+36916 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
