SOLUTION: If someone can please help me with this, it will be a huge help, thank you. 1) Given that f(x)= 0.25x^2 - 0.125x - 12.25 has a root at x = -6.75, use the axis of symmetry to fin

Question 1029211: If someone can please help me with this, it will be a huge help, thank you.
1) Given that f(x)= 0.25x^2 - 0.125x - 12.25 has a root at x = -6.75, use the axis of symmetry to find the other root of the function.
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

So then the vertex occurs at , which is also the location of the axis of symmetry.
So then the other root occurs at,

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) f(x)= 0.25x^2 - 0.125x - 12.25 has a root at x = -6.75
Here is the graph of this equation
:

:
the axis of symmetry is a vertical line intersecting the vertex
:
we know that the x coordinate of the axis of symmetry is
:
x = -b / 2a = -(-0.125) / (2(0.25)) = 0.25
:
The root x = -6.75 is one of two zeros of f(x) - to find the other zero, we calculate the distance -6.75 is from the x coordinate of the vertex
:
distance = |-6.75| + 0.25 = 7
:
*****************************************
therefore the other root is at x = 7.25
*****************************************
:
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