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)=ax2+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=ax2+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)=0.1x2.