Question 466195
graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). 
[Hint: If necessary, write f in the form f(x) = a(x – h)2 + k.] 
f(x) = –2x2 + 6x + 2
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 –2x^2 + 6x + 2
completing the square
-2(x^2-3x+9/4)+2+9/2
-2(x-3/2)^2+13/2
This is a parabola of the standard form, y=A(x-h)^2+k, with h=3/2 and k=13/2, and it opens downward.
see the graph of this parabola as follows:
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{{{ graph( 300, 300, -10, 10, -10, 10,-2(x-3/2)^2+13/2) }}}
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The next graph shows the result of removing the coefficient A=2. Notice how the curve is a little wider or less steep. The larger this coefficient, the steeper the curve.
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{{{ graph( 300, 300, -10, 10, -10, 10, -(x-3/2)^2+13/2) }}}

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The next graph shows the result of removing (h,k) the (x,y) coordinates of the vertex.
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{{{ graph( 300, 300, -10, 10, -10, 10, -x^2) }}}
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Removing the negative coefficient
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{{{ graph( 300, 300, -10, 10, -10, 10, x^2) }}}
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