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Calculus/How to find the vertex of a parabola

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Expert: - 2/25/2008


Question
I understand what a vertex is and how to find it on a graph or a graphing calculator but, do not know how to do it using an equation. The question is find the vertex of y=2x^2 +11x-6 I already know what the vertex is for the equation but, do not know how to show work for it without saying I used the calculator. I also know how to use the equation b/(-2a) but, when using it for the equation the x I get holds to be correct but, when I plug it into the equation to get the y the y turns out to become a number in the 50's instead of -21 as it should be. I am not sure if I am plugging it in wrong or if the equation just does not hold true for all problems.


More info.: I used the equation b/(-2a) to find the x coordinate and got -2.75 which checks with the graph. So theoretically if I have the x coordinate I should just be able to plug in the x into the equation y=2x^2 +11x-6 which would be y=2 * -2.75^2 + 11 * -2.75 - 6 then I found y to be -51.375 but, I know that it is incorrect because y should be -21. I also can not use the completing the square method so am trying to find an alternative route ergo b/(-2a).

Sarah

Answer
The first term is 2.75(-2.85)^2 = 15.125,
the second term is 11*-2.75=-30.25
and the third term is -6.

I think the mistake is in the first term where there is a negative squared, which makes it positive since your answere is off by about twice the first term.

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