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vazorg [7]
3 years ago
6

5^-2x times 5^x+2 = 5^-2x

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
3 0
5^{-2x}\cdot5^{x+2}=5^{-2x}\\
5^{x+2}=1\\
x+2=0\\
x=-2

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You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola.  The first few steps are as follows.  Set the parabola equal to 0 so you can solve for the vertex.  Separate the x terms from the constant by moving the constant to the other side of the equals sign.  The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out).  Let's start there.  The first 2 steps result in this polynomial:

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y=-a(x-h)^2+k

you can determine the coordinates of the vertex to be (1, 3)

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