A line with a slope of 3 intersects the quadratic function y=1/2x^2+2x-3 at exactly one point. Determine the coordinate of the y-intercept of the line.

Question

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Given:

How can I determine the values of A, and B? 

Answer 1

y intercept = - 3 1/2 = - 3.5 = - 7/2

line is y = 3x -3.5

y' = 3 = (.5x^2 +2x-3)' = x+2

x = 1, y = 1/2+2-3=--1/2

(1,-1/2) is where the line is tangent to the parabola

y=3x +b, plug in the point to find b=y intercept

-1/2 = 3+b

b = - 3.5