okay so what I'd like to cover for this one is how to graph f of X equals x squared minus 8x plus 15 so what I'm going to do is I'm gonna give you guys a little bit of a step-by-step process that I talked about to work this all right so ladies and gentlemen if you guys can follow this process I will kind of mix in some tips that you guys can use but let's try to make this Kent is easiest as it can be all right now you're gonna want to put that away so you can write this down and put it and pay attention so here we have x squared minus 8x plus 15 the first thing I want you guys would do is always just determine the axis of symmetry all right because remember all parabolas have an axis of symmetry right so the axis of symmetry remember is a vertical line so it's going to be x equals if you remember the opposite of B divided by 2a now before you forget what are a and B remember all quadratics come in the form of ax squared plus BX plus C so I write down my formula for my quat for my axis of symmetry and I know that B in this case is going to be negative 8 and a in this case is 1 so I'm just going to plug in my values so I have a negative negative 8 over 2 times 1 so I have negative negative 8 is a positive 8 divided by 2 equals 4 ok cool so that means my axis symmetry equals 4 so let's go ahead and graph that plot that right now yes questions ok where did I get 2a that is the formula for access symmetry that was in your notes we took last class period so I'm gonna draw this nice little dotted line because I remember that the axis of symmetry is going to be the line that's gonna split my graph into two Kriger at half right yeah all right so now I just need to determine some points so the next thing is make a table of values and determine I choose for you guys to determine at least two points to the left and two points to the right so we created a table of values so I'm sorry actually before I do that so I'm skipping ahead skip step number two is determine if our graph opens up or opens down so what we need to do to determine that is we needed need to determine what a is a is equal to one so therefore a is greater than zero right as one is greater than zero so by looking fat your previous notes when a is greater than zero your graph is gonna open up or open down open so your graph opens up therefore your vertex is going to be a maximum or a minimum okay so you guys now know that your graph opens up so you could kind of like put arrows right there it's going to open up and my vertex is going to be a minimum point so the next step which I started talking about prematurely is now to find our table of values all right so the first table of values or the first value if you guys remember how is the vertex related to the axis of symmetry does anybody remember how was your vertex relate to your axis symmetry hmm anybody remember last class period what is the x value of your vertex have to do with the axis of symmetry yes right remember ladies and gentlemen your vertex has to or your axis symmetry goes through your vertex right your vertex your axis symmetry goes through your vertex that means my vertex has to be on this line so the x value of my vertex is what for so I'll just pick one point four all right now what I'm gonna do is you guys can do the table values and let's so if I know my x value is 4 how do I determine my Y value and we're actually talking about a function so instead of Y values I'm gonna say f of we're gonna say it my f of X value so if I know my if I know X equal to 4 how do i Turman what my f of x value is going to be you plug it in right so you can say f of 4 equals 4 squared plus I'm sorry minus 8 times 4 plus 15 which equals 16 minus 32 plus 15 which equals negative 1 right so your vertex is at 1 2 3 4 negative 1 everybody following with that so I'm just gonna label that vertex ok now here's the next part that you guys can make easier or harder on yourselves all right really depending on what you want to do I tote I said in my directions to find 2 points to the left and 2 points to the right I don't really care which one you do first but try to find at least two points the left and two points to right then I'll show you guys a shortcut so what would be two points that are to the left of my axis symmetry you can do 3 to right you could do like negative 10 negative 20 Madison well ladies and gentlemen my advice is trying to do points that are very close to your vertex because a quadratic gets pretty large pretty quickly so I'm gonna pick the points 3 and 2 now you could say oh well that could be 5 and that could be 6 but before you do all the work let me little tip that you can do so if I want to find now the f of X value I do the same thing F of 3 equals 3 squared minus 8 times 3 plus 15 so you get 9 plus 15 24 minus 24 equals 0 so you could say after 3 equals 0 and then let's figure out what F of 2 is so that's going to be 2 squared minus 8 times 2 plus 15 so that one equals 3 right so could you just do the same for 5 & 6 yeah but let's let's use a little bit of our understanding of quadratics before we do that so if i graph 2 3 over 2 1 2 3 and then i graph 3 comma 0 i have this part of my quadratic right what does the axis of symmetry do again it splits it in half right so can I say that if this points here I have a direct symmetrical point on the other side yeah so I could say that then at 5 is going to be 0 and at 1 2 3 4 5 6 I'm gonna have 3 and there you go that's how you drop okay pretty cool yeah all right