How to Solve Quadratics & Conics Problems

Hi, I'm Rachel, and today we're going to be going over how to do quadratic and conic problems. So, there's a few different ways to solve these, but it's important to make sure that it's equal to zero, and that we have it in the form a x-squared plus bx plus c. That is the equation for quadratics. Now, the important thing to know is the quadratic formula because while factoring sometimes works for this, it doesn't always work. So the quadratic formula will always work no matter what, so it's a great thing to memorize. It is lengthy though, so listen up. The quadratic formula is x equals negative b plus or minus the square root of b-squared minus four ac, all over 2a. This is extremely important to memorize. So let's try it out. Let's say that we have zero equals, let's do 2x-squared plus 4x plus one. In this case, we have a equaling two, that's the first coefficient, b equals four, the second coefficient, and c equals one, the third variable at the end. So now let's plug this in to this, the quadratic formula, and see how it turns out. So we have x equals negative b, so that's negative four, plus or minus the square root of b-squared, so that's four-squared, that's gonna be 16, minus 4ac, that's four times times two times one, right, c, all over 2a. So that's two times a, which is two. Now if we simplify this out, we're gonna have 16 minus eight, that's gonna be square root of eight, if we, you know, use our knowledge of radicals, root eight can simplify to two to two, so we have negative four plus or minus two root two all over four, which we can simplify even more by taking out a two from the four and the two and the four, right? You can take out a two from all those numbers. So you get negative two, then you're dividing by two, plus or minus root two, right? Divided by two, all over two, divided by two. And that's our answer. And that's an example of a quadratic problem. I'm Rachel and thank you for learning with me today.