Question 178103: Which represents the range for -(y+3)=(x-4)^2 :
a){y such that y is less than or equal to -3,y belongs to a set of real numbers}
b){y such that y is greater than or equal to 4, y belongs to a set of real numbers}
c){y such that y is less than or equal to 3, y belongs to a set of real numbers}
d){y such that y is less than or equal to -4, y belongs to a set of real numbers}
I hope someone canhelp me, I always have trouble with these:(
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i would say the answer would be (a).
that would be:
y <= -3
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here's why
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your original equation is:
-(y+3) = (x-2)^2
multiply both sides of this equation by (-1) to get:
(y+3) = -(x-4)^2
subtract 3 from both sides of this equation to get:
y = -(x-4)^2 - 3
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y has to be negative because - (x-4)^2 will always be less than or equal to 0 regardless of the value of x.
if x is 4, (x-4)^2 = 0
if x is less than 4, (x-4) is negative but when you square it you get a positive number and when you take - the positive number you get a negative number.
if x is greater than 4, (x-4) is positive but when you square it, you still get a positive number and when you take - the positive number you get a negative number.
since - (x-4)^2 can never be positive, the most it can be is 0.
when it is 0, the value of y is -3.
that means that y can never be greater than -3.
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that means that (a) is the choice you want.
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