Desmos

Here is a desmos graph of a banana.

I can’t embed the desmos screen which is too bad, because the interactivity would be nice, but you can open it up in a different browser.

We can see if we can model the shape of the banana with a parabola.  Desmos has a lovely experimental approach, where you can write an equation and then manipulate sliders and watch how the graph changes.

See if you can find the perfect values for a, r, and s, and then see if you can figure out what those values do to the graph.

Here is a desmos graph of the water fountain.  To add the equation of the parabola, use the “+” button at the top left, and add an expression.  y=a(x-r)(x-s) and then you should see the slider option.  Select ALL and then slide them around to see if you can match the water fountain too.

What other parabolas do you see in your daily life?

Someone in the class determined the parabola that could best model their chin.