SOLUTION: Identify the vertex and line of symmetry for y=x^2-8x+11

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Question 207796: Identify the vertex and line of symmetry for y=x^2-8x+11
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=x%5E2-8x%2B11, we can see that a=1, b=-8, and c=11.


x=%28-%28-8%29%29%2F%282%281%29%29 Plug in a=1 and b=-8.


x=%288%29%2F%282%281%29%29 Negate -8 to get 8.


x=%288%29%2F%282%29 Multiply 2 and 1 to get 2.


x=4 Divide.


So the x-coordinate of the vertex is x=4. Note: this means that the axis of symmetry is also x=4.


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


y=x%5E2-8x%2B11 Start with the given equation.


y=%284%29%5E2-8%284%29%2B11 Plug in x=4.


y=1%2816%29-8%284%29%2B11 Square 4 to get 16.


y=16-8%284%29%2B11 Multiply 1 and 16 to get 16.


y=16-32%2B11 Multiply -8 and 4 to get -32.


y=-5 Combine like terms.


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


So the vertex is .