SOLUTION: Find the range of f(x) = −x2 − 6x − 7.

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Question 1130541: Find the range of
f(x) = −x2 − 6x − 7.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+-x%5E2+-6x+-7
here you have parabola that opens downward; so, it has a maximum at vertex
range will be all below y coordinate of the vertex
write your equation in vertex form:
f%28x%29+=+-%28x%5E2+%2B6x%29+-7
f%28x%29+=+-1%2A%28x%5E2+%2B6x%2Bb%5E2%29-1%2A%28-b%5E2%29+-7
f%28x%29+=+-%28x%5E2+%2B6x%2B3%5E2%29%2B3%5E2+-7
f%28x%29+=+-%28x%2B3%29%5E2%29%2B9+-7
f%28x%29+=+-%28x%2B3%29%5E2%29%2B2=> k=2 =>y coordinate of the vertex
then, range is:
{ f%28x%29 element R : f%28x%29+%3C=2 }

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%28x%2B3%29%5E2%2B2%29+