Question 126439
Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). 
y = –x² + 3x – 3
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First make the table:

x|-1| 0| 1| 2| 3| 4
y|-7|-3|-1|-1|-3|-7

Then we'll plot those points

{{{drawing(400,375,-4,7,-8,3,
locate(0-.1,-3+.3,o),
locate(1-.1,-1+.3,o),
locate(2-.1,-1+.25,o),
locate(3-.1,-3+.3,o),
locate(4-.1,-7+.3,o),
locate(-1-.1,-7+.3,o),
graph(400,375,-4,7,-8,3) )}}}

Next we'll calculate the axis of symmetry:

Rule:
The axis of syymetry of the graph whose equation is

y = Ax² + Bx + C

is the vertical line whose equation is 

x = {{{-B/(2A)}}}

You may not have learned about the vertex, but I'll
throw that in too.

Rule:
The vertex is the point

({{{-B/(2A)}}}, {{{-D/(4A)}}}), where D = B²-4AC

(D is called the "discriminant")

So in the case of 

y = –x² + 3x – 3

A = -1, B = 3, C = -3 

so the axis of symmetry is the vertical line
whose equation is

x = {{{-B/(2A)}}}

or

x = {{{-(3)/(2(-1))}}}

x = {{{-3/(-2)}}}

x = {{{3/2}}}

So we'll sketch in the
axis of symmetry:

{{{drawing(400,375,-4,7,-8,3,
locate(0-.1,-3+.3,o),
locate(1-.1,-1+.3,o),
locate(2-.1,-1+.25,o),
locate(3-.1,-3+.3,o),
locate(4-.1,-7+.3,o),
locate(-1-.1,-7+.3,o),
graph(400,375,-4,7,-8,3,0,999(x-3/2)) )}}}

and to find the vertex,

D = B² - 4AC
D = 3² - 4(-1)(-3)
D = 9 - 12
D = -3

So the vertex is the point

({{{-B/(2A)}}}, {{{-D/(4A)}}} or

({{{3/2}}}, {{{-(-3)/(4(-1))}}}, or

({{{3/2}}}, {{{3/(-4)}}}, or

({{{3/2}}}, {{{-3/4}}}),  

So we'll plot the vertex point too:

{{{drawing(400,375,-4,7,-8,3,
locate(3/2-.13,-3/4+.3,o),
locate(0-.1,-3+.3,o),
locate(1-.1,-1+.3,o),
locate(2-.1,-1+.25,o),
locate(3-.1,-3+.3,o),
locate(4-.1,-7+.3,o),
locate(-1-.1,-7+.3,o),
graph(400,375,-4,7,-8,3,0,999(x-3/2)) )}}}

Now we'll sketch in the graph, which is
a parabola:

{{{drawing(400,375,-4,7,-8,3,
locate(3/2-.13,-3/4+.3,o),
locate(0-.1,-3+.3,o),
locate(1-.1,-1+.3,o),
locate(2-.1,-1+.25,o),
locate(3-.1,-3+.3,o),
locate(4-.1,-7+.3,o),
locate(-1-.1,-7+.3,o),
graph(400,375,-4,7,-8,3,-x^2+3x-3,999(x-3/2)) )}}}  

Edwin</pre>