| Parabola Intersections |
Write the equation of the line containing the points of intersection of:
y = 2x2 - x -3
y = x2 + x + 5
Express your answer in y = mx + b form. |
Problem Moderated by: Douglas |
| Problem Solution |
The intersection points can be found by first solving the following:
2x2 - x - 3 = x2 + x + 5
x2 - 2x - 8 = 0
(x - 4)(x + 2) = 0
So x = 4 or x = -2
Substituting these two values back into the original equations gives us the following points of intersection:
(4, 25) and (-2, 7)
The equation of the line containing these points has a slope of FR{(25 - 7),{4 + 2)} = 3
So y = 3x + b. Plugging either point into the equation and solving for b gives us b = 13.
Thus the equation of the line is y = 3x + 13 |
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