SOLUTION: find the equation of the axis of symetry and the coordinates of the vertex of each quadratic function problem 1: g(x)= 2x squared - 12x+6

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Question 158118: find the equation of the axis of symetry and the coordinates of the vertex of each quadratic function problem 1: g(x)= 2x squared - 12x+6
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%5E2-12x%2B6, we can see that a=2, b=-12, and c=6.


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


x=%2812%29%2F%282%282%29%29 Negate -12 to get 12.


x=%2812%29%2F%284%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%5E2-12x%2B6 Start with the given equation.


y=2%283%29%5E2-12%283%29%2B6 Plug in x=3.


y=2%289%29-12%283%29%2B6 Square 3 to get 9.


y=18-12%283%29%2B6 Multiply 2 and 9 to get 18.


y=18-36%2B6 Multiply -12 and 3 to get -36.


y=-12 Combine like terms.


So the y-coordinate of the vertex is y=-12.


So the vertex is .