What is the range of the graph of y=-2x^2-8x-7 ?

Question

David · Accepted Answer

TTs160712_jen34016_1 
Function 
2( ) 2 8 7f x x x   
 
Now  
F(0) = -7
F(-infinity)= - infinity 
F(infinity)= + infinity 
Since the coefficient of square term is -2 and hence it will be a downwards parabola and will reach – 
infinity 
Now we have to find the maximum value of function 
Max value of parabola occurs at x= -b/2a = -(-8)/-4= -2 
F(-2)= -8 +16 -7 = 1 
And hence range is [ 1, - infinity ) 
Or it can be seen as
2 2
2
2
2
( ) 2 8 7 (2 8 7)
( ) [2( 4 4) 1]
( ) [2( 2) 1]
( ) 2( 2) 1
f x x x x x
f x x x
f x x
f x x
       
    
   
   
 
Now minimumvalue will be – infinity as square term is always positive so as x  tend to infinity or minus 
infinity f(x) will go to negative infinity 
Now max value of f(x) will occur when  square term has maximum value , maximum value of square tem 
will occur at x= -2 and the value will be zero and hence the maximum value of f(x) = 1 
So range is [ 1, -infinity)

What is the range of the graph of y=-2x^2-8x-7 ?

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