Find the values of x where the curve y = 8 -4x-2x^2 crosses the x-axis.
A curve crosses the x-axis when y=0, if we put that into the equation above we get the quadratic equation 0=8-4x-2x2. The solutions to this equation are the values of x where y=0, which is the same as saying the values of x where the curve crosses the y axis, so the solutions to this equation are our answers. We can solve the equation using the quadratic formula, x=(-b+√(b2-4ac))/2a or x=(-b-√(b2-4ac))/2a. In this equation a=-2, b=-4, c=8, which gives x=(-(-4)+√((-4)2-4*(-2)8))/2(-2) or (-(-4)+√((-4)2-4*(-2)8))/2(-2). Simplified this is x=(4+√80)/-2 or x=(4-√80)/-4, which again simplifies to x=-1+√5 or x=-1-√5. So these are values of x where the curve y=8-4x-2x^2 crosses the x-axis.
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