SOLUTION: What is the range of y = -x^2 - 2x + 3 A. x ≤ 4 B. x ≤ -4

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Question 1206777: What is the range of y = -x^2 - 2x + 3
A. x ≤ 4
B. x ≤ -4
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
What is the range of y = -x^2 - 2x + 3
A. x ≤ 4
B. x ≤ -4
~~~~~~~~~~~~~~~~~~~~~~ 

Function y(x) is a parabola opened downward.


The vertex is at  x =  = = " ' =  = -1.


The maximum value of  y(x)  is at  x = -1:   = -(-1)^2 - 2*(-1) + 3 = -1 + 2 + 3 = 4.



In case (A),  the value   = -1  is in the domain;  THEREFORE,

the  ANSWER  to (A) is :  at x <=4,  the range of  y(x)  is  (-oo,] = (-oo,4].



In case (B), the value of  = -1 is  out the domain of y(x);  THEREFORE,

    the  ANSWER  to (B) is :  at x <= -4,  the range of  y(x)  is  (-oo,y(-4)].

    y(-4) = -(-4)^2 - 2*(-4) + 3 = -16 + 8  + 3 = -5;  so,  the range of  y(x)  is  (-oo,-5].

Solved.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


One can only guess what the purpose of this problem is...

Exactly as shown, the problem makes no sense, because the range of a function is the set of y values it takes on; the two answer choices are both in terms of x.

If we guess that in fact the two answer choices were supposed to be in terms of y, then we only need to find the y coordinate of the vertex.

The x coordinate of the vertex is ; the y value at the vertex is

ANSWER (I guess...?):


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