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Question 224612: Given the parabola y = -(x – 6)^2 – 1, determine each of the following.
Identify whether the parabola y = -(x – 6)^2 – 1 opens up or down.
Identify the vertex of the parabola y = -(x – 6)^2 – 1.
Identify the x-intercept(s) of the parabola y = -(x – 6)^2 – 1.
Identify the y-intercept(s) of the parabola y = -(x – 6)^2 – 1.
Please help.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Given the parabola y = -(x – 6)^2 – 1, determine each of the following.
Identify whether the parabola y = -(x – 6)^2 – 1 opens up or down.
It opens down, the x^2 term is negative.
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Identify the vertex of the parabola y = -(x – 6)^2 – 1
y = -x^2 + 12x - 37
The vertex is at x = -b/2a = -12/-2 = 6
At x = 6, y = -1 --> vertex at (6,-1)
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Identify the x-intercept(s)
| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
The discriminant -4 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 -4 is + or -  .
The solution is  , or
Here's your graph:
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Identify the y-intercept(s)
-37
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