mooooom Posted January 4, 2011 Share Posted January 4, 2011 This is Chalkdust Precalc ch 2 test: Find the number of units x that produce a min cost C if C=0.01x^2-90x + 15000. The answer key is using a formula -b/2a ??? I was doing really well in math until this year, sigh. I watch the videos w/ the kids and work some of the problems myself, explain many more of them on the board... Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 4, 2011 Share Posted January 4, 2011 C has the form of a parabola: F(x)=ax^2+bx+c Algebra 1 should covered the solution of a quadratic equation F(x)=0, using the formula x=[-b +/- sqrt(b^2-4ac)]/2a If you look for the minimum of your cost function, that is the vertex of the parabola and the equation ax^2+bx+constant=0 has only one solution. (That is the case if the stuff under the sqrt is zero.) In that case, x will equal -b/2a Hope that helps. Quote Link to comment Share on other sites More sharing options...
Janice H Posted January 4, 2011 Share Posted January 4, 2011 The vertex is the lowest point of the upward (smiley way) quadratic curve. If you graph this quadratic equation of an upward facing parabola you would see that -b/2a is the first coordinate, the x value, of the (x,y) coordinates at the point of the vertex. Substitute this (-b/2a) x-value into the given equation to get the corresponding minimum cost. The b and a from the expression above come from the standard form ax^2 +bx +c =O. There are probably some maximum word problems in the chapter also. The same calculation for a downward curve gives the highest point. Now I just saw this has been answered, and that Regentrude neatly tied it to the quadratic formula. I'll leave this just in case it helps. Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 4, 2011 Share Posted January 4, 2011 As a side note: I'm pretty sure they include problems like this in precalculus so they can revisit them in Calculus and solve them much easier and more elegantly by just taking the derivative. Quote Link to comment Share on other sites More sharing options...
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