![]() So everything I just did, none of this is a good idea. The quadratic formula applies when the left hand side is equal to zero. Times one, times three, all of that over two times one. ![]() Root of b squared, which is 16, minus four Is equal to negative four plus or minus the square And so they'll immediately say, all right, I can recognize a here, as just being a one, there's a one coefficient Of b squared minus four ac, all of that over two a. The quadratic formula would say that the roots are gonna be x is equal to negative b plus or minus the square root They say, if I have something of the form ax squared plus bx plusĬ is equal to zero. A lot of folks would say, okay, I see a quadraticĮquation right over here. And that's also true if you're trying to apply So in order to factor like this and make headway in most cases, you're going to wanna have a zero on the right hand side over here. But remember, this would only be true if you're multiplying two things and you got zero as their product, then the solutions would be anything that made either one of Make this first term zero and negative one, or negative one would Another thing, try to do is, is they'll immediately say, okay, therefore x isĮqual to negative three or x is equal to negative one because negative three will Something times something is equal to negative one doesn't help you a ton. But they either make a mistake or they realize that And then they either areĪbout to make a mistake, this is actually algebraically valid. This left hand expression, say that's going to be x plus three times x plus one, and then that's going toīe equal to negative one. That add up to four and whose product is three. See something like this, let me rewrite it. You'll sometimes see people use, especially when they But if can't make these things disappear, this strategy that I've just outlined is not going to be a productive one. But if you have an x term like this and it doesn't cancel out somehow, you know, if there was anotherįour x on the other side, then you could subtractįour x from both sides, and they would disappear. Then this strategy would have worked assuming that there are some solutions. In fact, it would have worked if you did not have Now, there's some cases in which this strategy would have worked. You still don't know what x is, and it's really not clear what to do with this algebraically. Of negative four x minus four, but this still doesn't help you. And you could get something like this, you would get x is equal to plus or minus the square root The plus of minus of one side to make sure you're Square root of x squared is equal to, and you could try to take And now, someone might say, if I take the square root of both sides, I could get, I'll just write that down. And then what happens? On the left hand side, you do indeed isolate the x squared, and on the right hand side, you get negative four x minus four. Isolate that x squared by subtracting four x from both sides and subtracting three from both sides. So you could imagine, let me just rewrite it. People will try to go for is to isolate the x squared first. So just willy nilly, taking the square root ofīoth sides of a quadratic is not going to be too helpful. ![]() ![]() ![]() Isolate the x over here? You've pretty quickly hit a dead end. But even if this wasĪ positive value here, how do you simplify or how do you somehow Even if this wasn't a negative one here, that's the most obvious problem. Plus four x plus three is equal to the square The square root of both sides? And if you did that, you would get the square root of x squared So one strategy that people might try is, well, I have something squared, why don't I just try to take I have something on both sides of an equal sign. Why is it a quadratic equation? Well, it's a quadratic because it has this secondĭegree term right over here and it's an equation because Use a table of values and a given graph to find the solution to a quadratic equation.- In this video, we're gonna talk aboutĪ few of the pitfalls that someone might encounter while they're trying to solve a quadratic equation like this. The student is expected to:Ī(8)(B) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formulaĪ(8)(A) write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems The student formulates statistical relationships and evaluates their reasonableness based on real-world data. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. Let's investigate ways to use a table of values to represent the solution to a quadratic equation.Ī(8) Quadratic functions and equations. ![]()
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