SOLUTION: find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x)=4x^2-40x+104

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)=4x^2-40x+104      Log On


   

Question 329083: find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x)=4x^2-40x+104
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square to convert to vertex form, y=a%28x-h%29%5E2%2Bk where (h,k) is the vertex.
f%28x%29=4x%5E2-40x%2B104
f%28x%29=4%28x%5E2-10x%29%2B104
f%28x%29=4%28x%5E2-10x%2B25%29%2B104-4%2825%29
f%28x%29=4%28x-5%29%5E2%2B4
Comparing to the equation above,
(h,k)=(5,4)
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The vertex lies on the axis of symmetry, x=5
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The min or max value occurs at the vertex.
Since the coefficient of the x%5E2 term is positive, the parabola opens upwards and the vertex value is a minimum.
ymin=4
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