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# finding the range of a function watch

1. Q. g(x)=x^2+2ax+2 ,xER

find the range of g in terms of a

i dont know how to work this out, can someone show me a step to step method on how to do this please. thankyou
2. differentiate to find the minimum

2x + 2a = 0
x = -a

so the smallest value g(x) can be (i.e. the range) is -a (i think)
3. (Original post by Pheylan)
differentiate to find the minimum

2x + 2a = 0
x = -a

so the smallest value g(x) can be (i.e. the range) is -a (i think)
the answer should be g(x)>/ 2-a^2
4. could complete the square to find min also.
5. (Original post by klgyal)
the answer should be g(x)>/ 2-a^2
yeah i'm not great at finding ranges
6. Complete the square!!!!!!!!!!!!!!!!!!!!!!!!!! !111111111111111111111111ONE!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!

7. (Original post by Pheylan)
differentiate to find the minimum

2x + 2a = 0
x = -a

so the smallest value g(x) can be (i.e. the range) is -a (i think)
The smallest value g(x) can take isn't that, what it is is g(-a).
8. the answer should be g(x)>/ 2-a^2
Indeed, the value of the formula at is . This is minimum because the coefficient of is positive.

In general, the x coordinate of the min (or max) of the parabola is .
9. (Original post by Slumpy)
The smallest value g(x) can take isn't that, what it is is g(-a).
ooh i see, thanks

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