SOLUTION: What is the vertex in the equation x^2 - 6x + 4?

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Question 644011: What is the vertex in the equation x^2 - 6x + 4?
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%5E2-6x%2B4, we can see that a=1, b=-6, and c=4.


x=%28-%28-6%29%29%2F%282%281%29%29 Plug in a=1 and b=-6.


x=%286%29%2F%282%281%29%29 Negate -6 to get 6.


x=%286%29%2F%282%29 Multiply 2 and 1 to get 2.


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.


f%28x%29=x%5E2-6x%2B4 Start with the given equation.


f%283%29=%283%29%5E2-6%283%29%2B4 Plug in x=3.


f%283%29=9-6%283%29%2B4 Square 3 to get 9.


f%283%29=9-18%2B4 Multiply -6 and 3 to get -18.


f%283%29=-5 Combine like terms.


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


So the vertex is .