[math-fun] "Elementary/H.S." applications of quadratic formula?
I can easily come up with elementary applications of square roots, but are there any (many?) elementary/high school applications of the quadratic formula? The things I came up with are a bit artificial: cannon ball trajectories, drag strip race cars, bicycle wind resistance. I seem to recall some quadratic equilibrium equations from H.S. chemistry, but that isn't very elementary. (Helping to solve cubic eqns doesn't count!!)
I can easily come up with elementary applications of square roots, but are there any (many?) elementary/high school applications of the quadratic formula?
Find the dimensions of the rectangle with area A and perimeter P. Solution: Solve x^2 - (P/2)x + A = 0. This generalises to an elementary application of Cardano's formula, namely finding the dimensions of the cuboid with volume V, surface area S and total edge length L: x^3 - (L/4)x^2 + (S/2)x - V = 0. Sincerely, Adam P. Goucher
Nice, but who in high school today would care about areas & perimeters of rectangles? Perhaps 150 years ago, farmers would worry about acreage and fence lengths, but today?? At 03:10 AM 8/1/2012, Adam P. Goucher wrote:
I can easily come up with elementary applications of square roots, but are there any (many?) elementary/high school applications of the quadratic formula?
Find the dimensions of the rectangle with area A and perimeter P.
Solution: Solve x^2 - (P/2)x + A = 0.
This generalises to an elementary application of Cardano's formula, namely finding the dimensions of the cuboid with volume V, surface area S and total edge length L: x^3 - (L/4)x^2 + (S/2)x - V = 0.
Sincerely,
Adam P. Goucher
On Tue, Jul 31, 2012 at 5:06 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I can easily come up with elementary applications of square roots, but are there any (many?) elementary/high school applications of the quadratic formula?
Most sports involve parabolic motion somewhere. Ask kids to estimate Michael Jordan's hang time (the time in the air during a jump) and you'll usually get answers ranging from a second to ten seconds; they're really surprised when you ask them to count during a video. There's a simple mat in many gyms that will measure the height of your jump by timing it; it's a puzzle at first to figure out how it knows how high you jumped, since there's no laser rangefinder or anything like that. It's also very visceral. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
In a discussion of "golden ratio calipers" ( www.goldenmeancalipers.com , www.quantumbalancing.com/goldenmeantemplate.htm , many others - just google it ) I was asked how to get from the classical "the ratio of the smaller to the larger, is the ratio of the larger to the whole" to 1.618. A no-more-than-H.S. math listener remarked that was the only time in his life that he had seen the quadratic formula used for anything. - John On July 31, 2012 at 8:06 PM Henry Baker <hbaker1@pipeline.com> wrote:
I can easily come up with elementary applications of square roots, but are there any (many?) elementary/high school applications of the quadratic formula?
participants (4)
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Adam P. Goucher -
Henry Baker -
J J -
Mike Stay