SOLUTION: ok so my question is how can you still use the "answer" you get from the Quadratic formula to find the vertex? And this is what i did... Problem: y= x^2-4x+6 i used the quadra

Question 130120: ok so my question is how can you still use the "answer" you get from the Quadratic formula to find the vertex? And this is what i did...
Problem: y= x^2-4x+6
i used the quadratic formula...
x= 4(+or-) / 2(1)
and got x= 2 - 1.415i and x= 2 + 1.415i
how can i use those conjugate pairs to find the vertex?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the x-coordinate of the vertex, simply average the two roots.

Add the two roots

Group like terms

Combine like terms

Simplify

So it turns out that when you add any two complex conjugates together you will get a real answer.

Now divide the answer by 2

So the x-coordinate of vertex is 2

note:
Remember the quadratic formula is

and the formula for the x-coordinate of the vertex is . Notice if you add the two roots the square root part cancels out to to give you . So this shows how the quadratic formula and the vertex are related.
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