Positive square root of 8, or it could be the negative Sides, and, of course, you want to take the positiveĪnd the negative square root, because 4x plus 1 could be the We can take the square root ofīoth sides of this equation. Sides of this equation? And this is just kind We add 8 to both sides of this equation? Then the left-hand side of theĮquation becomes 4x plus 1 squared, and these And how do we do that? Well, what happens if Time, because you might see something interestingįactoring it. Of these must be equal to 0, so x could be that or that. X minus something, times x minus something else Then subtract 8 from the constant you get out here, and Now, based on everything we'veĭone so far, you might be tempted to multiply this out, Video that we're going to do on completing the square. Special form, and it's really a bit of warm-up for the next Several examples of quadratic equations that are really of a With some of these "honing" skills, you may not be able to see the reasons, whys and wherefores at the moment, but that will come in time. Right now you are honing your skills at algebra, which will never leave your side no matter how far up the math ladder you want to climb, algebra is there. You see, we can model much of the world via functions and this type of analysis helps us understand the model, which in turns helps us understand the nature of what we are trying to model, which gives us a better understanding of nature itself. Later, in calculus, you will learn to take the derivatives of functions and try to find where the derivatives are zero as well, and when we find them, it tells us even more about the behavior of the function such as how fast it changes from negative to positive or vice-versa, and where the maximum/minimum value is or if it even exists.Īll this procedure is part of a mathematical process called analysis, which is really what math is all about. It tells us something about the behavior of the function, for example, once we know where the zeros are, we can look on either side of the zero values and find out if the function is positive or negative, which in turn gives clues to where maximum and minimum values may be lurking. Why all this trouble to find where functions are zero?
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