## Quadratic Functions in the Real World

Posted by in DP Math on Wednesday, November 21st, 2012 at 11:10 pmQuadratics is not just what we learn in Geogebra, or our math textbooks. It is everywhere around us. Quadratics can be used to model real life objects that we see almost everyday. An example is a banana…

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Above shows how quadratic function can model the natural shape of a banana. This is done by using Geogebra. I inputed a picture of a banana which shows a great parabolic shape in Geogebra. I then resize, rotate, and adjust the picture to fit the coordinates on the graph. Insert different points of the parabolic shape of the banana, as a clearer guide later.

Now, we know that a parabolic shape must have a quadratic function, therefore an equation in standard form of *f(x)=ax ^{2}+bx+c*. To find an equation for the parabolic shape of the banana, we need to find the values of a, b, and c.

We can do this by using a slider in Geogebra, and name them *a, b*, and *c*. Then, input the equation *y=ax ^{2}+bx+c* in the input box, and adjust the values for

*a*,

*b*, and

*c*on the slider until it best fits the points, or the parabolic shape of the banana itself.

From the banana picture above, we can see that a quadratic function is able to model the banana quite accurately, with *a=0.1*, *b=0, *and *c=0.* Therefore, the equation is *f(x)=0.1x ^{2}.*

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I love it Jesslyn. Great piece of work.

cool, thanks