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put this solution on YOUR website!Identify the axis of symmetry, create a suitable table of values, and then sketch the graph (including the axis of symmetry).
y = –x^2 + 3x – 3
Complete the square on the x-terms as follows:
x^2-3x+? = -(y+3)+?
? = [ (1/2) the coefficient of the 1st degree term]^2 :
? = [(1/2)(-3)]^2 = 9/4
Replace ? with 9/4 to get:
x^2-3x+(9/4) = -y-3+(9/4)
Factor the left side ; simplify the right side to get:
(x-(3/2))^2 = -y-(3/4)
(x-(3/2))^2 = -(y+(3/4))
This form shows you the vertex and axis of symmetry of the parabola
The vertex is ((3/2),(-3/4))
The axis of symmetry is x=(3/2)
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Table of values for y = –x^2 + 3x – 3
If x=0, y=-0^+3*0-3 = -3
if x=1, y=-1^2+3*1-3 = -1
if x=-1, y=-(-1)^2-3*-1-3 = 1
etc.
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Identify the axis of symmetry, create a suitable table of values, and then sketch the graph (including the axis of symmetry).
y = x^2 – 4x
x^2-4x+? = y+?
? = [(1/2)(-4)]^2 = 4
x^2-4x+4 = y+4
(x+2)^2 = y+4
Vertex is (-2,-4)
Axis of symmetry is x=-2
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To generate a table of values choose x-values around x=-2 like -1.-2
0,1; substitute them one at a time into y = x^2 – 4x to find the
corresponding y-values.
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Cheers,
Stan H.
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