SOLUTION: Find the vertex, the line of symestry, the maximum or minimum value of quadratic function, and graph the functions f(x)=-2x^2+2x+3

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Question 334220: Find the vertex, the line of symestry, the maximum or minimum value of quadratic function, and graph the functions
f(x)=-2x^2+2x+3

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-2x%5E2%2B2x%2B3
Complete the square to convert to vertex form, y=a%28x-h%29%5E2%2Bk where (h,k) is the vertex.
f%28x%29=-2x%5E2%2B2x%2B3
f%28x%29=-2%28x%5E2-x%29%2B3
f%28x%29=-2%28x%5E2-x%2B1%2F4%29%2B3%2B1%2F2
f%28x%29=-2%28x-1%2F2%29%5E2%2B7%2F2
Vertex:(1%2F2,7%2F2)
The vertex lies on the axis of symmetry,x=1%2F2.
The vertex value is the function max or min depending on whether the parabola opens upwards or downwards.
The sign of the x%5E2 term determines direction of opening.
Positive upwards, negative downwards.
Since the coefficient is -2, the parabola opens downwards and the vertex value is a maximum.
ymax=7%2F2
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