Question 531804: I need to find out the maximum or minimum of the function f(x)=-2x^2+4x+8. Then, I have to find the domain and range. So far, I have found that the domain equals all real numbers.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I need to find out the maximum or minimum of the function f(x)=-2x^2+4x+8. Then, I have to find the domain and range. So far, I have found that the domain equals all real numbers.
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Standard form of equation for a parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. If the lead coefficient<0, parabola opens downward, that is, it has a maximum.
For given equation: f(x)=-2x^2+4x+8, parabola opens downward.
By inspection you can see there are no restrictions, so the domain is all real numbers as you stated. To find the range, we need to find the maximum and you can do this by completing the square.
y=-2x^2+4x+8.
y=-2(x^2-2x+1)+8+2
y=-2(x-1)^2+10
vertex: (1,10)
maximum at 10
ans:
Range: (-∞,10)
Domain(-∞,∞)
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