Word Problems With Quadratics

Thursday

On Thursday, 4/4, we learnt about solving word problems that would require us to use the quadratic formula. To refresh your memory, if it's not already memorized, here is the quadratic formula:

At the beginning of class we split off into groups that we would later make notability projects with. Before that we did the homework problems up on the board.

This is the problem that my group worked on:

A deck of uniform width has area 72m^2 and surrounds a swimming pool that is 8m wide and 10m long. Find the width of the deck.

It always help to draw out the problem to figure out how to solve it.

Above are the steps we went through to solve the problem using the equation "length x width = area". Our length is 8 + 2x because we know that the pool is 8 m wide but there are also two areas of x on both side of the pool. The width is 10 + 2x for the same reason. When we multiply these two we get 72 + 80 because the problem says the deck's area is 72 and we can find the area of the pool by multiplying 8 and 10. After simplifying the problem we get an equation that we plug into the quadratic equation and simplify until we get x = (-9 +/- 3sqrt17)/2, since lengths can be negative, we know that the sign before the root is +, not -. We plugged this into our calculator and got close to 5/3.

After doing these problems we sat down with our groups and started working on more word problems.

Friday

On Friday we finished on our group word problems. Here is the problem that my group worked on, shown in a notability note:

This problem was solved much like the example I showed before, we set up the problem much like any other word problem, trying to solve the x variable, and then when we got to the quadratic we plugged it into the quadratic formula and simplified some more. Since this is the blog you can't hear the recording that is in our project but if you want to hear it, or see any of the other projects from other groups I would recommend going and checking out the dropbox where the all are.

Thanks for reading, hope you learnt a lot!

-Rowan