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1. Intro quad formula and discriminants

Added May 17, 2020 •

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Intro to quadratics and discriminants. Look at website: https://www.mathsisfun.com/algebra/quadratic-equation.html for more info

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I algebra Wednesday she was going to be just a quick tutorial other than the other videos I posted on the quadratic formula and using the discriminant and what that means now we skip chapter 8 which all about graphing quadratics which is the parabolas and it really is a shame there's a lot of in a real world examples on this ties in with physics and playing and using the force of gravity I'm not what this means on a graph what you guys have been doing in the last few sections when you're solving a quadratic is finding the solutions and then finding the Solutions really what we're finding are the x-intercepts and that's where the graph crosses the x-axis so the x-axis is the horizontal axis so you'd be looking here in here calling for in the last few IXL in the last few IXL ones we did this a little bit with factoring in the zero product property it finds the same thing so Solutions or X another name for that has roots it all means the same thing in terms of quadratic other pieces of a parabola with the vertex of a quadratic which kind of messing with the graphing but for now we're just going to focus on those Solutions and what that means so if we have a quadratic equation that we're trying to solve so I'm going to use the example of 5x squared + 6x + 1 is equal to 0 we want to find okay where does it cross the x axis what we need to do first to use the quadratic formula if you need to make sure that everything is on one side it's in this form ax squared plus BX plus C where a B and C are the coefficients the numbers in front of the variable No Label it so a is 5 Deus Ex PS1 quadratic formula it looks in a really complicated Master P I always like to sing it to Pop Goes the Weasel so I ended up sending it it'll probably ahead of time but it looks like this tax is equal to negative B plus or minus the square root of B squared minus 4AC and yes it's awful we were in class I'd be singing that'll why I'd be making you guys seen that does help you kind of to remember and if you've already done that I solve by completing us really is just from that I'm so when we played everything in our a SIV is 60 is one so we have negative 6 instead of 6 Plus what's the square root of B squared so 6 squared minus 4 times a day which is 5 x c which is one and then all over 2A 30 * 5 we're going to simplify that so negative 6 minus now you remember order of operations with exponents first six squares 36 fly before we add or subtract so 4 * 5 * 1 is 20 number 10 so 36 - 20 + 16 over 10 16 is 4 and when we solve for this one so this gives us to answers and I could cry so we would do -6 + 4 divided by 10 which would be -2 / 10 which would be -1 that would be one of our Solutions which is the same as -2 and then our other one is going to be -6 - 4/10 which is -10 / 10 which is -1 because our age I use positive we have a parabola going up and that means that our two x-intercepts we've got one at negative and it was positive want to be a point to so here so we something that looks like that and then this would be at our point to I'm sorry that should be a negative point two I can I have the how to say this is -1 and then that's it be like negative point to right there we have something like that and have you been in class and spent more time even on chapter we would spend more time in finding the outlet on and you will I'm in Algebra 2 you know you might talk a little bit about in Geometry but more than likely Algebra 2 okay now getting on to the discriminant the discriminant has to do this number right in here under the square root sign so the discriminant is just a part the quadratic formula B squared minus 4AC now there's three cases now if this number is a positive number that means we are going to have two solutions and with the example that we just did 36 - 20 is 16 so that we can take the square root of 16 which is 4 even if it was a messy number like √ 11 that's fine it's still a positive number he would still have two solutions or answers would just be a little messy because we have that with her formula I have the both the plus and the minus sign there now it's underneath the radical is a negative number we have no Solutions because we can't take the square root of a negative I think we talked a little bit about that in class we have negative one on there it's called an imaginary number you're going to talk more about imaginary numbers in Algebra 2 and our usefulness but what that kind of means on a graph if we have a parabola that means that its never get across and see their prey that's about the x axis or it's a parabola going down that's below the act the x-axis is it'll never cross no Solutions there to solution it's going to be something like we did up here this is two solutions a discriminant was positive okay so we have three cases positive negative or third case is if discriminant is 0 0 you look back at our formula here that means that the plus or minus square 2-0 is just 0 so all you have 40 way you have one solution so if the discriminant is 0 then we have one Solutions and what that looks like on a graph is where that Middle Point the graph and we call it the vertex is the only point where it touches the x-axis so that would beat this case over here so sometimes if we're just looking for the shortcut is just to use this part of it so the part that's underneath the square root B squared minus 4AC you can kind of use this as your cheat sheet as you're using your IXL hopefully some of that kind of sticks in your head when you do move on to Algebra 2 but working with the rabbit and how to simplify those you'll use those a lot with geometry for next year

Uploaded by Nikola Leibold.

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1. Intro quad formula and discriminants

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