Question 535744: What are the vertex, the axis of symmetry, the x any y intercepts and the domain and range of the following function? f(x)=2x^2-2x-4
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What are the vertex, the axis of symmetry, the x any y intercepts and the domain and range of the following function? f(x)=2x^2-2x-4
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y=2x^2-2x-4
complete the square
y=2(x^2-x+1/4)-4-1/2
y=2(x-1/2)^2-9/2
This is an equation of a parabola of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
For given equation:
lead coefficient>0 means parabola opens upwards and has a minimum
vertex:(1/2, -9/2)
axis of symmetry: x=1/2
..
y-intercept
set x=0
y=-4
x-intercept
set y=0
2(x-1/2)^2-9/2=0
2(x-1/2)^2=9/2
divide by 2
(x-1/2)^2=9/4
take sqrt of both sides
x-1/2=±3/2
x=1/2±3/2
x=2
or
x=-1
..
Domain: (-∞,∞)
Range: (-9/2,∞)
see graph below as a visual check on the answers:
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