Quadratic Equation Exercises

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photograph quadratic equation exercises 1

Quadratic Equation Exercises

Many students will just get everything on one side as we’ve done here and then get the values of a, b, and c based upon position.  In other words, often students will just let a be the first number listed, b be the second number listed and then c be the final number listed.  This is not correct however.  For the quadratic formula a is the coefficient of the squared term, b is the coefficient of the term with just the variable in it (not squared) and c is the constant term.  So, to avoid making this mistake we should always put the quadratic equation into the official standard form.
quadratic equation exercises 1

Quadratic Equation Exercises

This is a quadratic, and I’m supposed to solve it. I could multiply the left-hand side, simplify to find the coefficients, plug them into the Quadratic Formula, and chug away to the answer.
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Quadratic Equation Exercises

In general, you first check to see if there is an obvious factoring or if there is an obvious square-rooting that you can do. If not, then it’s usually best to resort to the Quadratic Formula. But (warning!) don’t only use the Quadratic Formula; while it will always give you the answer — eventually — it is not always the fastest method. And speed can count for a lot on timed tests.
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Quadratic Equation Exercises

First, we MUST have the quadratic equation in standard form as already noted.  Next, we need to divide both sides by a to get a coefficient of one on the x2 term.

Quadratic Equation Exercises

When you’re solving quadratics in your homework, you can often get a “hint” as to the “best” method to use, based on the topic and title of the section. For instance, if you’re working on the homework in the “Solving by Factoring” section, then you know that you’re supposed to solve by factoring. But in the chapter review and on the test, you don’t know which section the quadratic came from. Which method should you use?
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Quadratic Equation Exercises

This one doesn’t factor (since there are no factors of (–4) = –4 that add to +1), and this isn’t formatted as “(squared part) equals (a number)”, so I can’t use square-rooting to solve. This leaves me with completing the square (yuck!) or the Quadratic Formula. I’ll use the Formula:

Quadratic Equation Exercises

Now, this isn’t quite in the typical standard form.  However, we need to make a point here so that we don’t make a very common mistake that many student make when first learning the quadratic formula. 
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Quadratic Equation Exercises

As with all the other methods we’ve looked at for solving quadratic equations, don’t forget to convert square roots of negative numbers into complex numbers.  Also, when b is negative be very careful with the substitution.  This is particularly true for the squared portion under the radical.  Remember that when you square a negative number it will become positive.  One of the more common mistakes here is to get in a hurry and forget to drop the minus sign after you square b, so be careful.
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Now, in this case don’t get excited about the fact that the variable isn’t an x.  Everything works the same regardless of the letter used for the variable.  So, let’s first get the equation into standard form.

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