hi can someone show me all steps to find the vertex of this equation using standard to factored form with some extra steps in between and from standard to vertex form directly. Thanks it is very much appreciated
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First we factor out -120 and get y = -120*(x^2 + 19/15*x + 6/15)
Now the expression x^2 + 19715*x + 6/15 = (x - a)^2 + b = x^2 - 2ax + a^2 +b gives us the position of the vertex.
It must be -2ax = 19/15 and a^2 + b = 6/15. So we have a = -19/30 and b = 6/15 - a^2 = -1/900. So the vertex has the coordinates x = -19/30 and y = 120*(-1/900) = 2/15
Now the expression x^2 + 19715*x + 6/15 = (x - a)^2 + b = x^2 - 2ax + a^2 +b gives us the position of the vertex.
It must be -2ax = 19/15 and a^2 + b = 6/15. So we have a = -19/30 and b = 6/15 - a^2 = -1/900. So the vertex has the coordinates x = -19/30 and y = 120*(-1/900) = 2/15