SOLUTION: Find the vertex of the parabola y=-2xto the second power+ 12x-13=?

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Question 206764: Find the vertex of the parabola y=-2xto the second power+ 12x-13=?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=-2x%5E2%2B12x-13, we can see that a=-2, b=12, and c=-13.


x=%28-%2812%29%29%2F%282%28-2%29%29 Plug in a=-2 and b=12.


x=%28-12%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x=3 Divide.


So the x-coordinate of the vertex is x=3. Note: this means that the axis of symmetry is also x=3.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


y=-2x%5E2%2B12x-13 Start with the given equation.


y=-2%283%29%5E2%2B12%283%29-13 Plug in x=3.


y=-2%289%29%2B12%283%29-13 Square 3 to get 9.


y=-18%2B12%283%29-13 Multiply -2 and 9 to get -18.


y=-18%2B36-13 Multiply 12 and 3 to get 36.


y=5 Combine like terms.


So the y-coordinate of the vertex is y=5.


So the vertex is .