SOLUTION: Find the vertex, the line of symmetry, the maxiumum or minimum value of the quadratic function, and graph the function.
f(x)=-2x^2+2x+3
The x-coordinate of the vertex is:
The y-
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Question 352607: Find the vertex, the line of symmetry, the maxiumum or minimum value of the quadratic function, and graph the function.
f(x)=-2x^2+2x+3
The x-coordinate of the vertex is:
The y-coordinate of the vertex is:
The equation of the line of symmetry is x=
The maximum/minimum of f(x) is:
The value, f(1/2)=7/2 is minimum or maximum?
So far, I have tried to work the problem. This is what I have:
f(x)=-2x^2+2x+3, so you use (-b/2a,4ac-b^2/4a)
Therefore, if -b/2a=-(2)/2(-1)=1
Then put 1 back into the equation.
f(1)=-2(1)^2+2(1)+3
Using FOIL, I come up with 1.
This where I get confused. Is the x-coordinate 1? How do i come up with y-coordinate?
Is the line of symmetry also 1?
I think I confuse myself the most when I try to apply the FOIL method?
Any help is so very much appreciated! Thanks in advance!
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Complete the square to put the quadratic equation into vertex form, where (,) is the vertex.
So the vertex is (,).
The vertex lies on the axis of symmetry,
The value at the vertex is either a minimum (when ) or a maximum (when ).
In this case, .
.
.
.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the vertex, the line of symmetry, the maxiumum or minimum value of the quadratic function, and graph the function.
f(x)=-2x^2+2x+3
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vertex occurs at x = -b/(2a) = -2/(2*-2) = 1/4
This is a maximum
The x-coordinate of the vertex is:1/4
The y-coordinate of the vertex is:f(1/4) = 3.375
The equation of the line of symmetry is x= 1/4
The maximum/minimum of f(x) is: max = 3.375
The value, f(1/4)=3.375 is maximum because the coefficient of x^2 is negative.
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Cheers,
Stan H.
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