Question 960120
you have to group the x^2 and x together to get:


y = (3x^2 - 24x) - 46


you have to factor out the 3 so that the x^2 term has a coefficient of 1.


y = 3 * (x^2 - 8x) - 46


you have to complete the squares on (x^2 - 8x)


divide the coefficient of the x term by 2 and you will get 4.


square the 4 and you will get 16.


(x^2 - 8x) will become equal to (x-4)^2 - 16


3 * (x^2 - 8x) - 46 will become equal to:


3 * ((x-4)^2 - 16) - 46 which will become equal to:


3 * (x-4)^2 - 48 - 46 which will become equal to:


3 * (x-4)^2 - 94.


that's the vertex form of the equation.


you started with:


y = 3x^2 - 24x - 46


you ended up with:


y = 3 * (x-4)^2 - 94


those two equations are equivalent.


if you graph both equations, they will generate the same graph.


that graph is shown below:


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