Changing Quadratic Equation from Standard form to Vertex Form

I went back to moomoomath we are going to learn how to change a quadratic function from standard form to vertex form so let's write the two forms out okay standard form is y equals ax squared plus BX plus C vertex form is y equals a notice the A's are the same times X minus H quantity squared plus K so I have a perfect square in here where H and K is the vertex of my parabola and that's why it's called vertex form because I can actually identify my vertex from it so here we are and we have y equals negative 2x squared plus 14x minus 8 and I want to convert it to this other form well the most important point on a parabola is the vertex so I have a little formula and it's negative B over 2 times a and that will give me the x coordinate of my vertex so let's identify a and B let's see a in this case is negative 2 and B is positive 14 so let's plug those in the opposite of B is a negative 14 times 2 times a of negative 2 so that's gonna give me what negative 14 over negative 4 which is 7 halves who like a deflection that's alright though I know what I know I can handle this so now I'm going to take this x-coordinate and I'm gonna plug it back into the original function and that's gonna give me my y-coordinate so let's see if we can handle our fractions negative 2 times 7 halves all squared plus 14 times 7 halves and notice I've plugged in 7 halves twice in for both X's and then minus 8 so let's clean this up that's going to be giving me negative 2 times 49 fourths so negative 2 over 1 times 49 fourths plus let's see 2 those into 14 seven times so that's going to give me plus 49 and then minus now we just got to do a little bit more cleaning up here okay that's gonna give me four goes into to kind of cancel those out and so I've got that's it negative 49 halves plus 49 plus 8 okay now you can grab your handy dandy calculator or you could have actually put it in back here if you had wanted to I'll see what's half of 49 that's gonna give me twenty nine and a half and it's negative plus 49 plus eight we're actually minus eight isn't it that's a minus eight so it's gonna give me 41 I'm adding in the back so negative 29 plus four and a half plus 41 that's gonna give me what eleven and a half so positive eleven and a half is my y-coordinate so let's go back and write that as an ordered pair so my ordered pair would be let's see the vertex is that's negative seven halves or no that's positive seven house and then positive 11.5 now I've got one written as a fraction and a decimal so we may want to make them all the same let's make them all decimals okay I'm gonna take those two and plug them into the vertex form where H is my x-coordinate K is my y-coordinate to get my vertex form so y equals a what was our a hmm what was our a our a is negative two so let's plug in negative 2 times X minus H well that seven halves are three and a half I'll write it as a decimal for now plus K well K is my y-coordinate plus eleven point five and that is how you convert from standard to vertex now what all of them be this messy with fractions no I actually have a second one over here that you might want to try it's 3x squared plus 12x plus seven and see if you can use your negative B over two a to find in this case a pretty nice coordinate I believe the x-coordinate is going to be negative two and then you can plug in negative two and find the y-coordinate hope this video was helpful on teaching you how to change forms