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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E2%2F4-x%2F8-49%2F4
f%28x%29=%281%2F4%29%28x%5E2-x%2F2%2B1%2F16%29-49%2F4-1%2F64
f%28x%29=%281%2F4%29%28x-1%2F4%29%5E2-784%2F64-1%2F64
f%28x%29=%281%2F4%29%28x-1%2F4%29%5E2-785%2F64
So then the vertex occurs at x=1%2F4, which is also the location of the axis of symmetry.
So then the other root occurs at,
x=1%2F4%2Babs%281%2F4-%28-6.75%29%29
x=1%2F4%2B7
x=7.25

Answer by rothauserc(4718) About Me  (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
:
+graph%28+300%2C+200%2C+-8.2%2C+8.7%2C+-12.50%2C+5%2C+0.25x%5E2+-+0.125x+-+12.25%29+
:
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
:
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therefore the other root is at x = 7.25
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