Algebra 2 -Conics

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The directions are : Write each equation in standard form (if needed), then find appropriate information for the particular conic.

the question: y=2x^2-12x+19

HOW DO I BEGIN???

Complete the square and rewrite as
y = 2x^2-12x + 19
= 2(x^2 - 6x + 9)+ 19 - 18
= 2(x-3)^2 + 1
This is an upward-pointing parabola with its lowest point at x=3, y+1
If you define new coordinates as
y'= y-1 and x' = x-3,
the equation becomes
y' = 2 x'^2

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