What is the distance between the points of intersection of the graphs y= [x^2 ]

Mathematics
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What is the distance between the points of intersection of the graphs y=   and y= 6-x

a. √26                                 c. 2√37

b. 5√2  d. √170

I started by setting the equations equal to each other and solving for x, which gave me 2 and -3.  Then, I plugged these x-values back in and got the coordinate points (2,3) and (-3,-12).  Then, using the Pythagorean Theorem (distance formula), I tried to get the distance between the two points.

√[(-3-2) + ] = √ 

I ended up getting the square root of 250, or 5 on the square root of 10 equals c.  Of course, this isn't one of the answer choices.  I'd like to know where I went wrong (or if I did it totally wrong), and how I can correctly solve the equation
May 12th, 2015

this step is wrong.

Then, I plugged these x-values back in and got the coordinate points (2,3) and (-3,-12).


On plugging the value of x you should be getting (2,4) and (-3,9)
you can use y =x^2 to find the above values of 4 and 9

distance of (2,4) and (-3,9) = sqrt[(2-(-3))^2 + (4-9)^2] = sqrt ( 5^2 + (-5)^2) = sqrt(25+25) = 5√2


Hope this helps :)

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May 12th, 2015

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