Solving Problems Using Quadratic Equations

Solving Problems Using Quadratic Equations-41
You've now seen it all when it comes to projectiles! Hopefully you've been able to understand how to solve problems involving quadratic equations.I also hope that you better understand these common velocity equations and how to think about what this problem looks like graphically in order to help you to understand which process or formula to use in order to solve the problem.Therefore, this is the only correct answer to this problem.

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Since I'll be cutting equal-sized squares out of all of the corners, and since the box will have a square bottom, I know I'll be starting with a square piece of cardboard.

In this last exercise above, you should notice that each solution method gave the same final answer for the cardboard's width.

Note that the second value could have been gotten by changing the sign on the extraneous solution.

Warning: Many students get in the very bad habit of arbitrarily changing signs to get the answers they need, but this does not always work, and will very likely get them in trouble later on.

Since the ball reaches a maximum height of 26.5 ft, we know that it will reach a height of 20 feet on the way up and on the way down.

Let's just estimate on our graph and also make sure that we get this visual in our head.

And many questions involving time, distance and speed need quadratic equations.

These word problems involve situations I've discussed in other word problems: The area of a rectangle, motion (time, speed, and distance), and work.

Let's take a look at the picture "in our mind" again. This is the calculation for when the ball was on the ground initially before it was shot.

This actually never really occurred because the ball was shot from the cannon and was never shot from the ground. The other answer was 2.54 seconds which is when the ball reached the ground (x-axis) after it was shot.

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