Solving Problems Using Quadratic Equations

Solving Problems Using Quadratic Equations-8
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. Just don't forget that when you solve a quadratic equation, you must have the equation set equal to 0.

There are many types of problems that can easily be solved using your knowledge of quadratic equations.

You may come across problems that deal with money and predicted incomes (financial) or problems that deal with physics such as projectiles.

The first sentence says one is the square of the other, so I can write The sum is 132, so Plug into and solve for B: The possible solutions are and .

The difference of two numbers is 2 and their product is 224.

But the Quadratic Formula took longer and provided me with more opportunities to make mistakes.

Warning: Don't get stuck in the rut of always using the Quadratic Formula!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. Now you have to figure out what the problem even means before trying to solve it.I completely understand and here's where I am going to try to help!Therefore, this is the only correct answer to this problem.Yes, this problem is a little trickier because the question is not asking for the maximum height (vertex) or the time it takes to reach the ground (zeros), instead it it asking for the time it takes to reach a height of 20 feet.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.However, these problems lead to quadratic equations. You can solve them by factoring or by using the Quadratic Formula.

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