You have the term y=x^2+4x+2. A line y=t*x+q crosses it in the points P and Q. Define t so that the sum of the distance of the two points from the x axis is minimal.
Is this a trick question and there two points are at the same point, the apex of the quadratic function? If not, how would I go about figuring it out?
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Anonymous2011-01-19 13:09
Actually, that would be the base of the parabola, but that's nit-picking. The base of the parabola occurs at -2, -2.
What kind of answer is the problem looking for, is what you should be asking? If you graph the parabola and then play with drawing sloped lines, you'll find two kinds of solutions. A general minimized summed-distance line occurs when only one of the points has y = 0 (the line, parabola, and x-axis all intersect at this point); the slope of the line carries it over to intersect with the other side of the parabola. (Another case involves translating the tangent of the parabola at any given point but it is much more situational since it only produces ideal answers near y = 0 and the base.)