SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=2x^2-8x+19

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=2x^2-8x+19      Log On


   

Question 329090: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=2x^2-8x+19
Answer by Fombitz(32388) About Me  (Show Source):
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Complete the square to convert to vertex form, y=a%28x-h%29%5E2%2Bk where the vertex is (h,k).
f%28x%29=2x%5E2-8x%2B19
f%28x%29=2%28x%5E2-4x%2B4%29%2B19-2%284%29
f%28x%29=2%28x-2%29%5E2%2B11
Comparing,
(h,k)=(2,11)
The vertex lies on the axis of symmetry, x=2.
The vertex y value is the function's max or min value.
The sign of the x%5E2 coefficient determines whether it's max or min.
Since the coefficient of x%5E2 is positive, the parabola opens upward and the vertex value is a minimum.
ymin=11
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