SOLUTION: sketch a graph of the following (find and include focal points, verticies, asymptotes, directrix, as appropriate). Estimate any irrational values on the graph. 1. y = 2x^2

SOLUTION: sketch a graph of the following (find and include focal points, verticies, asymptotes, directrix, as appropriate). Estimate any irrational values on the graph. 1. y = 2x^2 - 10x

Question 74682: sketch a graph of the following (find and include focal points, verticies, asymptotes, directrix, as appropriate). Estimate any irrational values on the graph.
1. y = 2x^2 - 10x + 27
first i tried to get all of the x and y's to one side, then complete the square, but i didn't know how because y in this problem is not squared...but i tried it anyway and got... 27/4 (y-27)= x^2 - 5x + 25/4 ...i'm not sure where to go from here>???
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
y = 2x^2 - 10x + 27
This is the equation of a parabola opening up.
2(x^2-5x+(5/2)^2) = y - 27 + 2*(25/4)
2(x-(5/2))^2 = y-58/4
2(x-(5/2))^2 = y-29/2
(x-(5/2))^2 = (1/2)(y-29/2)
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4p=1/2 ; p=1/8
Vertex at (5/2,29/2)
Focus at (5/2, 29/2 + 1/8) = (5/2, 117/8)
Directrix: y=29/2 - 1/8 ; y=115/8
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Cheers,
Stan H.

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