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+2x+8

Algebra ->  Quadratic Equations and Parabolas -> 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+2x+8      Log On


   

Question 330509: Find the vertex,the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x)=-2x^2+2x+8
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square to put the equation in vertex form, y=a%28x-h%29%5E2%2Bk. where (h,k) is the vertex.
f%28x%29=-2x%5E2%2B2x%2B8
f%28x%29=-2%28x%5E2-x%29%2B8
f%28x%29=-2%28x%5E2-x%2B1%2F4%29%2B8%2B2%281%2F4%29
f%28x%29=-2%28x-1%2F2%29%5E2%2B17%2F2
The vertex is (1%2F2,17%2F2).
The vertex lies on the axis of symmetry x=1%2F2
The max or min value occurs at the vertex.
Since the coefficient for the x%5E2 term is negative, the parabola opens downward and the vertex value is the maximum.
ymax=17%2F2
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