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Lesson 9.2 #24

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Okay, classroom and help you with number 24 now from lesson 9.2. We start off with the 16 + x squared. 8x and like we mentioned before we want to avoid a leading proficient. That's negative because at this point. We're not thinking of it in terms of graphing. There's no why equal if it's just a quadratic equation, so nice simplify it I would like my quadratic equation to have a positive leading proficient. I'm actually going. Stop by adding 8x.  Over to both sides and then we riding this left side in standard form so that it says. x squared + 8x + 16 rearranging my terms using the commuter property of addition equals 0 so now I have My quadratic equation in standard form and now I'm going to graph it as a quadratic function by replacing the 0 with a y equals. At the why right below it and do that in blue. And the first step that I like to do when graphene is since I'm looking for exeter ships. I like to see if I can factor out this particular. Polynomial or try to mom left hand side like we did when we factored in chapter 7 so that I could rewrite this function in intercept form so off to the side? Make a little x factor. I'll put 16 of top that's multiplied team deleting proficient times constant term and 8 down below and you can see. Way that I'm going to have positive for as my factors since my leading coefficient is a positive one I can quit. rewrite this function and intercept form using  My middle terms. I here so I will write x+ X x + 4 + noticed that this is actually a perfect square trade a bill and I have a square foot by normal Pattern which I can see right here, so I'm okay. Write it intercept form it's also appropriate to write it as x + 4 squared equals. Why you? This point this helps me a lot because I'm able to write intercept form I know a couple of things right now. I know that my x intercept I have one. It's going to be whatever could make this by no milk equal to 0 it's going to be opposite of positive for cuz -4 if I replace, Texas. peter for -4 + 4 give me 0 and that would actually gave me my intercepts that the x intercept is that -4 and it only one of them is actually going to be my lucien  to migration x equals -4 and I know what you want to do you want just quit right now. I'm just highlight it and be done and A question students always ask me the y if we know the answer do we have to continue graphic. We have to prove it by graphing and make sure that our grass does show that it has exactly. X intercept at -4 so sorry to call that's why I'm get it with you okay, so I have my accent. I said that -4. I need to find my access this. Emma we had this an intercept form which comes by the way from less than 8..  5 I believe I could add mighty + 2 / 2 so this would be so my my exodus up in this case would be. -4  plus -4 divided by 2 which you can see it's going to be -8. By the way, too.  Which again is -4 and that's usually what happens in this case as I have my intercept. It's also my first text. Which is awesome. I access the symmetry and we're going to find all of that out right now so that we can grass.  So I have 1x in there. So this graphic going to sit right on the x axis at -4 which makes sense that's the vertex cuz it's phyllis Klein my grass and the taxes in symmetry goes. s***, which is a vertical line at -4 so to double check with your vertex you would plug -4 back into your original occasion and self. But you'll still get 0 but we'll double-check it.  So -4  where -4  Plus 16 equals why so this would be? - 32 + 16 equal why you'll get -16 + 16 equals why? So if you go a little bit further why would equal 0 which kind of already worked out for us in the end so our vertex? also going to be -4, 0 and I have everything I need. Rap and I already have what I think is the answer the solution. To this quadratic equation, but I'm a cell by graphing to continue. my girl  when you get my cell or line letting make it black, and it must start with see my why access over here. My Ex Ex sister here. the number by 2 so I have a -2 and a -4 + -6 + -8  posits Just one.  Alright, so right now what I have is I have an x intercept 3 here. I have an axis of symmetry. Coming right through this crappy get my axis of symmetry drawn. It's also my vertex. Only other question now is what next all I have is 1.5. My first text. It's actually my exercise and then axis of symmetry, but I need more points, so we Figure out what how do we get our other point? And it's pretty simple. Just like we did before we can come back up to this value of see right here and call it what? Dance which is C. Which is also our y intercept and we can use the y intercept together annex point? So have the number my y axis now, and I'll member it by 8 so. 816  2411 that place so now I can have a point at 16 reflected across. axis of symmetry  to graph  so are purpose again today. It feels very much like Chuck. This case from our graphing. We're graphing to prove the solution of a quadratic equation, so we don't actually start with a quadratic function. There's no value of why there's no function notation at the back. It's just a quadratic equation. We must first simplify it and right. It's excuse. In standard form then graph at as a quadratic function to see how many places it will cross our way excuse me Rx access or if it? X access at all like we found out in a previous problem.  So I highlighted our solution our solution is x equals -4 that is. Let me put it right here. We have proving that with our graph. So that's all of her work.

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Lesson 9.2 #24

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