You have to prove that the product is equal to 16.

y=x^2-2 is the parabola

y=mx is one of the lines because the line goes through the origin and thus b=0

set the right sides equal to each other

x^2-2=mx

x^2-mx-2=0

solve for x using the quadratic equation

[m±√(m^2+8)]/2

these are 2 of the 8 x-values

[m+√(m^2+8)]/2 and [m-√(m^2+8)]/2

now multiply these two values together and you get...

[m^2-(m^2+8)]/4

(m^2-m^2-8)/4

-8/4=-2

no matter what the slope "m" is, "m^2" gets cancelled out and you are always left with -2

the second line, no matter what it is, no matter what the slope is, will yield another -2 (don't forget that the lines always go through the origin)

the third line gives another -2

the fourth line gives another -2

you get -2 four times for the four x-values

(-2)(-2)(-2)(-2)=16

Majd A.

Really helps. Thanks!01/07/20