SOLUTION: Function & graph: The two curves are the branches of the graph of y=1/x. The straight line intercepts the x-axis at point (-1,0) and the y-axis at point (0,2).it also cuts the c

Algebra ->  Functions -> SOLUTION: Function & graph: The two curves are the branches of the graph of y=1/x. The straight line intercepts the x-axis at point (-1,0) and the y-axis at point (0,2).it also cuts the c      Log On


   

Question 982936: Function & graph:
The two curves are the branches of the graph of y=1/x. The straight line intercepts the x-axis at point (-1,0) and the y-axis at point (0,2).it also cuts the curves at points A and B. Find the coordinates of point A and of point B.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The line has slope 2 and y-intercept is given. The line has the equation y=2x%2B2.

The intersection points A and B will be for 1%2Fx=2x%2B2 formed by equating the two expressions for y. This will be a quadratic equation giving two x coordinates.

2x%2B2=1%2Fx
2x%5E2%2B2x=1
2x%5E2%2B2x-1=0

Discriminant is 2%5E2-4%2A2%2A%28-1%29=4%2B8=12.
x=%28-2%2B-+sqrt%2812%29%29%2F4
x=%28-2%2B-+2%2Asqrt%283%29%29%2F4
x=%28-1%2B-+sqrt%283%29%29%2F2

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The two points to be found, still unfinished, would be as these:

x=%28-1-sqrt%283%29%29%2F2 and y=2%2F%28-1-sqrt%283%29%29
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x=%28-1%2Bsqrt%283%29%29%2F2 and y=2%2F%28-1%2Bsqrt%283%29%29.


graph%28300%2C300%2C-4%2C4%2C-4%2C4%2C1%2Fx%2C2x%2B2%29