Question 515325: find the vertex, the line of symetry, the max/min value of the quadratic unction and graph.
f(x)=2x^2-8x+5
vertex=
line of symetry equation=
max or min of f(x)=2x^2-8x+5
is it max/min=
graph=
thank you!
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! f(x) = 2x^2 -8x +5
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The vertex has the x coordinate = -b/2a.
Solve for 'y' to get the ordered pair.
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f(x) = y
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x = -b/2a = -(-8)/(2*2) = 8/4 = 2
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y = 2(2^2) -8*2 +5
y = 8 -16 +5
y = -3
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The vertex is (2,-3).
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We know the parabola opens 'up' so the vertex will be the minimum value of f(x).
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The line of symmetry is the vertical line that passes through the vertex, dividing the parabola into two symmetric halves.
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x = 2 would do it. Note that for any value of 'y', x =2. The slope is undefined because x-x1=0, by definition, so the line is vertical.
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To determine the maximum of minimum, you also can take the first deriviate and set it = 0.
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dy/dx = 4x-8
4x = 8
x = 2
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The maximum (or minimum) occurs at x=2. We know from above that the vertex is (2,-3). So that confirms it is a minimum.
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You also should consider the roots.
y = 2x^2-8x+5 cannot be factored.
So you can use the quadratic equation.
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(-b +sqrt(b^2-4ac)) / 2a and (-b -sqrt(b^2-4ac)) / 2a
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| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=24 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 3.22474487139159, 0.775255128608411.
Here's your graph:
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