Question 821955: f(x) = -3x^2+2x-1
Fine the vertex and axis of symmetry.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
f(x) = -3x^2 + 2x - 1
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the above quadratic equation is in standard form, with a=-3, b=2, and c=-1
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-3 2 -1
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two complex roots at:
x = 0.333333333 + (-0.471404521)i
x = 0.333333333 - (-0.471404521)i
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the quadratic vertex is a maximum at: ( 0.333333333, -0.666666667 )
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NOTE ON CALCULATING THE QUADRATIC VERTEX:
vertex-x = -b/(2a) = -2/(2(-3)) = 2/6 = 0.333333333
vertex-y = -D/(4a), where D= bb - 4ac
vertex-y = -(bb - 4ac)/(4a)
vertex-y = -(4 - 4(-3)(-1))/(4(-3))
vertex-y = -(4 - 12)/(-12)
vertex-y = -(-8)/(-12)
vertex-y = -0.666666667
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the axis of symmetry is: x = 0.333333333
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NOTE ON CALCULATING THE AXIS OF SYMMETRY:
axis of symmetry is a vertical line at: x = -b/(2a) = -2/(2(-3)) = 2/6 = 0.333333333
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as you can see, the algebra matches the solver's results perfectly
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