SOLUTION: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y = –x^2 + 3x – 3

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Question 103593: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).
y = –x^2 + 3x – 3
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
there is no x intercept
y intercept is -3.0 (if x=0 => y=-3)
x1 and x2 have a real and imaginary part
x2=1.5 +.866i+i
x2=1.5 - .866i+i
vertex%28h%2Ck%29
h=-b%2F2a
h=-3%2F2%2A%28-1%29
h=3%2F2=1.5
k=+y%28h%29
k=-1%2A%283%2F2%29%5E2+%2B3%283%2F2%29+-3
k=-9%2F4+%2B9%2F2+-3
k=9%2F4+%96+3
k=2.25-3
k=-0.75
vertex 1.5, -.75
table:
y = –x^2 + 3x – 3
x | y
0 | -3
1 | -1
2 | -1

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B3x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A-1%2A-3=-3.

The discriminant -3 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -3 is + or - sqrt%28+3%29+=+1.73205080756888.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B3%2Ax%2B-3+%29