SOLUTION: Consider the function f(x)=x^2+4x+1 Find h, the x-coordinate of the vertex of this parabola So I took -b/2a or -4/2(1)^2=-4/2 So I believe h=-2 The next part of the question is

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Question 124130: Consider the function f(x)=x^2+4x+1
Find h, the x-coordinate of the vertex of this parabola
So I took -b/2a or -4/2(1)^2=-4/2
So I believe h=-2
The next part of the question is: Substitute the two integers immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.
x y
_________
_________
h =__
_________
_________

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
One minor comment to your work as noted below:
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Consider the function f(x)=x^2+4x+1
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Find h, the x-coordinate of the vertex of this parabola
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So I took -b/2a or -4/2(1)^2=-4/2 <=== don't square the (1). The denominator is just 2*(1)
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So I believe h=-2 <=== correct
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The next part of the question is: Substitute the two integers immediately to the left and
right of h into the function to find the corresponding y. Fill in the following table. Make
sure your x-values are in increasing order in your table.
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(I'm going to use periods as "space holders only" in the table. They are just to keep the table formatted.
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The two integers to the left of h = -2 are x = -4 and x = -3. The two integers to the right
of h = -2 are x = -1 and x = 0
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You are to substitute these 5 values (-4, -3, -2, -1, and 0) for the value of x in the equation:
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Table:
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... x .... y
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.. -4 ... +1 <=== Note that y = (-4)^2 + 4*(-4) + 1 = +16 - 16 + 1 = +1
.. -3 ... -2 <=== Note that y = (-3)^2 + 4*(-3) + 1 = +9 - 12 + 1 = -2
.. -2 ... -3 <=== x is h and therefore y = (-2)^2 + 4*(-2) + 1 = 4 - 8 + 1 = -3
.. -1 ... -2 <=== y = (-1)^2 + 4*(-1) + 1 = 1 - 4 +1 = -2
... 0 ... +1 <=== y = 0^2 + 4*0 + 1 = 0 + 0 + 1 = +1
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Notice the values of y for values of x that are equal distance from x = -2. When x = -4 and x = 0
the values of x are both 2 units away from x = -2. And the values of y at these two distances
are both +1.
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Similarly when x = -1 and x = -3 both these values are 1 unit away from x = -2. And in both
these cases y = -2.
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This is also shown in the graph of y = x^2 + 4x + 1 which is shown below. The vertical green
line through x = -2 represents the line of symmetry, which in this case means that if you
printed this graph out and then folded it along the vertical green line, the two sides of the
graph would be exactly on top of each other.
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Hope this helps you to understand what I think you are being taught ... namely what symmetry
means. Notice the horizontal lines I put on the graph. If you look at each horizontal line
and the points where the graph intercepts them you will see that the distance between those
intersections and the green line are equal on both sides of the green line of symmetry.
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That's sort of what symmetry means. The graph on one side of the green line is the "mirror image"
of the graph on the other side of the green line.
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