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# Two parabolas are the graphs of the equations \$y=2x^2-10x-10\$ and \$y=x^2-4x+6\$.. Give all points where they intersect. List the points in or

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Two parabolas are the graphs of the equations \$y=2x^2-10x-10\$ and \$y=x^2-4x+6\$.. Give all points where they intersect. List the points in order of increasing \$x\$-coordinate, separated by semicolons.

Guest Jan 16, 2018
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To solve this, set the functions equal

2x^2 -  10x - 10  =  x^2  - 4x  +  6       rearrange as

x^2 -  6x -  16  =  0      factor as

(x - 8)  ( x + 2)  = 0

Setting each  factorto 0 and solving for x, we have that x  = 8  and x  = -2

So....using   x^2  - 4x +  6   we can find the two y values

(-2)^2  -4(-2)  +  6  =  18  ⇒  (-2, 18)

8^2  -  4(8)   +  6    =  38  ⇒  (8, 38)

CPhill  Jan 16, 2018
edited by CPhill  Jan 16, 2018

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