Can anyone help me with a Precalc problem?

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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...

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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.

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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.

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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.

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