SOLUTION: Find the coordinates of the vertex for the parabola given by the equation f(x)=-x^2-2x-1

Algebra ->  Functions -> SOLUTION: Find the coordinates of the vertex for the parabola given by the equation f(x)=-x^2-2x-1      Log On


   

Question 635819: Find the coordinates of the vertex for the parabola given by the equation f(x)=-x^2-2x-1
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the coordinates of the vertex for the parabola given by the equation f(x)=-x^2-2x-1
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Do it like this one:
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Find the coordinates of the vertex for the parabola given by the equation
f(x)=-3x^2-x-1.
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The vertex is on the LOS, Line of Symmetry, or the Axis of Symmetry
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The LOS is x = -b/2a
x = 1/-6 = -1/6
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f(-1/6) = -1/12 + 1/6 - 1 = -11/12
--> vertex (-1/6,-11/12)


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

general form:
f%28x%29=ax%5E2%2Bbx%2Bc...where a cannot be zero
you are given:
f%28x%29=-x%5E2-2x-1
the x-coordinate of the vertex is -b%2F2a
We need only to find that coordinate, and then find the y-coordinate that goes with it by using that value for x in our equation for f%28x%29.
so, x=-b%2F2a where a=-1 and b=-2
x=-%28-2%29%2F2%28-1%29
x=2%2F-2
x=-1.....now find y
f%28-1%29=-%28-1%29%5E2-2%28-1%29-1
f%28-1%29=-1%2B2-1

f%28-1%29=-2%2B2

f%28-1%29=0

the vertex is at (-1, 0)


+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+-x%5E2-2x-1%29+