Question 75697This question is from textbook Beginning Algebra
: For each equation in exercises 25 to 28, identify the axis to symmetry, create a suitable table of values, and sketch the graph (including the axis of symmetry).
y=-x^2+6x-2
I am needing some assistance with this problem. I am not quiet sure how to find ths symmetry and need further help. Thanks.
This question is from textbook Beginning Algebra
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Find the axis of symmetry: The axis of symmetry is the line that divides the curve represented by this equation, into two mirror-halves.
 Since your equation is already in the standard form of:
 you can find the axis of symmetry which is given by:
 In this case, a = -1 and b = 6
 The axis of symmetry is the line represented by the equation x = 3.
If you graph this, it would be a vertical line passing through the point (3, 0)
For creating the table of points, you select a value for the independent variable (that's x), substitute this into your equation and solve for the corresponding value of y. This will give you the (x, y) of one point. Do this several times to get several points for your table.
Then you plot these points on a piece of coordinate graph paper on which you have previously drawn the x-axis and the y-axis.
Here's an example of how you would generate one of these ponts:
Pick a value for x: x = 0 and substitute this into your equation and solve for y.
Set x = 0
 For x = 0, y = -2
So, for one of the points, you have (0, -2)
Do this for a few more points then plot them on graph paper and sketch the graph. The graph should look like this:
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