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Two parabolas are the graphs of the equations y = 2x^2 - 7x - 1 and y = 8x^2 - 2x - 5. Give all points where they intersect. List the points in order of increasing x-coordinate, separated by semicolons.

 Jan 4, 2022
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Give all points where they intersect.

 

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\(2x^2 - 7x - 1 = 8x^2 - 2x - 5\\ 6x^2+5x-4=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x = -{-5 \pm \sqrt{25+4\cdot 6\cdot 4} \over 2\cdot 6}=-\frac{5\pm 11}{12}\\ x \in \{\frac{1}{2},-\frac{4}{3}\}\\ y\in \{-4,11\frac{8}{9}\}\)

The parabolas intersect at the points:

\(P_1(\frac{1}{2},-4);P_2(-\frac{4}{3},11\frac{8}{9})\)

laugh  !

 Jan 4, 2022

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