Let's start off with something that we could haveįactored just to verify that it's giving us the You're actually going to get this solution and that And you might say, gee, this isĪ wacky formula, where did it come from? And in the next video I'm Reasonable formula to stick in your brain someplace. Get a lot more practice you'll see that it actually is a pretty And I know it seems crazy andĬonvoluted and hard for you to memorize right now, but as you X is equal to negative b plus or minus the square root ofī squared minus 4ac, all of that over 2a. Tells us that the solutions to this equation are General quadratic equation like this, the quadratic formula The coefficient on the x to the zero term, or it's Squared term or the second degree term, b is theĬoefficient on the x term and then c, is, you could imagine, Where a, b and c are- Well, a is the coefficient on the x So let's say I have an equationĬ is equal to 0. Solve for the roots, or the zeroes of quadratic equations. Show you what I'm talking about: it's the quadraticįormula. Things and not know where they came from. Prove it, because I don't want you to just remember Memorize it with the caveat that you also remember how to Videos, you know that I'm not a big fan of memorizing Really!Įxpose you to what is maybe one of at least the top five They got called "Real" because they were not Imaginary. NOTE: The Real Numbers did not have a name before Imaginary Numbers were thought of. Meanwhile, try this to get your feet wet: "What's that last bit, complex number and bi" you ask?! The term "imaginary number" now means simply a complex number with a real part equal to 0, that is, a number of the form bi. The name "imaginary number" was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless. They have some properties that are different from than the numbers you have been working with up to now - and that is it. Well, it is the same with imaginary numbers. It seemed weird at the time, but now you are comfortable with them. Remember when you first started learning fractions, you encountered some different rules for adding, like the common denominator thing, as well as some other differences than the whole numbers you were used to. They are just extensions of the real numbers, just like rational numbers (fractions) are an extension of the integers. ![]() Note that the quadratic formula actually has many real-world applications, such as calculating areas, projectile trajectories, and speed, among others.Don't let the term "imaginary" get in your way - there is nothing imaginary about them. This is demonstrated by the graph provided below. Furthermore, the quadratic formula also provides the axis of symmetry of the parabola. The x values found through the quadratic formula are roots of the quadratic equation that represent the x values where any parabola crosses the x-axis. Recall that the ± exists as a function of computing a square root, making both positive and negative roots solutions of the quadratic equation. Below is the quadratic formula, as well as its derivation.įrom this point, it is possible to complete the square using the relationship that:Ĭontinuing the derivation using this relationship: Only the use of the quadratic formula, as well as the basics of completing the square, will be discussed here (since the derivation of the formula involves completing the square). A quadratic equation can be solved in multiple ways, including factoring, using the quadratic formula, completing the square, or graphing. For example, a cannot be 0, or the equation would be linear rather than quadratic. The numerals a, b, and c are coefficients of the equation, and they represent known numbers. ![]() Where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. In algebra, a quadratic equation is any polynomial equation of the second degree with the following form: Fractional values such as 3/4 can be used.
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