This morning I was trying to come up with some good problems for students to use to find local maxima and minima. It's an awesome feeling to be able to combine everything I know about graphs and polynomials and end behavior to create polynomials within the window that I want that do what I want. It's cool to think that I don't have to just guess random things. So the graph is too long and skinny? I can do a vertical compression or a horizontal stretch. I want two local maxes and one local minimum, so I know I need to give it a negative leading coefficient and an even degree. It might be neat to come up with some sort of guidelines and have the students come up with their own polynomials. I wouldn't want them to just guess and check though. I might have them write something that says what they would have to do to a graph to get the desired results. It really forces you to use everything you know about polynomials and graph behavior and actually apply it.
I've been working on creating a visual to go with Psalm 91 in desmos (a free online graphing software). Here's what I've come up with so far: I tried to show the fowler's snare (bottom left), deadly pestilence/plague/Corona virus (bottom right), the fortress of the Most High, an eagle with wings to give us refuge and protection, and a shield and rampart to represent God's faithfulness which will protect us from the "arrow that flies by night." To make my picture, I've typed in 181 mathematical equations so far. Here are just a few of them so you can get a better idea of what I'm talking about even if you don't totally understand the equations. I was reflecting (for the thousandth time) on how my understanding of mathematics leads me to a deeper understanding of God and his power. When I was first learning how to graph I started by plotting points. If I wanted to graph just one single line, I might graph two or all of these points an...
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