MA DoR ST-9A 2016-2024 free printable template
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Okay one the big problems we're going to look with is actually how do we get something into the graphing form because when a graph is in standard form a lot of times going to have enough information to be able to use it so graphing form gives us a lot of advantage it's like it helps us to figure out what the vertex is or even to be in potentially solvent so first of all understanding reforms standard form your problem is y equals ax squared plus BX plus C this is a great form if you have to go over and possibly factor it if you want to use quadratic formula notice an B and C but when you're going to graph this is not that easy to graph, so we want to change it to graphing for graphing or also called vertex form is y equals a times X minus H squared plus K now notice this parts really important the A's are the same a these two values are the same so if I have the standard form of parabola and I wanted the graphing form I already know my stretching factor' the HE is not the same as B and C them in particular we're a lot of students make mistakes I think k is the same as C, but it's not so gotta be a little careful of that so let's go over, and we're going to look at three different methods for going over and changes them from standard form into graphic form okay the first method were going to look at is the idea of averaging the x-intercepts, so we're going to do is we're going to take this equation and this is a good method if its easy equation to factor so this one factors pretty easily need two numbers that multiply to give me negative 3 but add to give me negative 2 so X minus 3x plus 1 so solving letting this equals 0 i get x equals 3 and x equals negative 1, so the actual points are 30 and negative 10, so graphically this is what's happening we have those x-intercepts now if you look at these halfway between those two intercepts we went over imagine you know you have a line going across halfway between my vertex occurs so halfway between is basically averaging, so I'm going to add these two numbers together and divide by two, so I do three plus negative one that gives me 2 divided by 2 gives me one that gives me the x-coordinate of my vertex now I need to find the y-coordinate, and it's real important you always want to plug back into my original equation even though it would still work by plugging the second one is always safe is to always plug back into the original equation, so I'm going to do one square minutes 2 times 1 minus 3 when I do this I get 1 minus 2 minus 3 so 1 minus 5 is negative for the y-coordinate then is negative 4, so that tells me I basically have a parabola that's shifted to the right one and then down for so my equation is y equals x minus 1 squared members an opposite four shifts left and right x minus 1 squared and then minus 4 can this one was good it was easy to do because it was factorable so what do you do when it's not factorable, or it gets a little more complex that's why we want to look at some other methods...
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