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.

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Parabola Intersections 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

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

Fractional Infinite Series