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Math Help - Weird inequalities?

  1. #1
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    Weird inequalities?

    A function is defined by f(x) = x^2+2x+c. Find the value of the constant c for which the range of f is given by f(x)≥ 3
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    Quote Originally Posted by Punch View Post
    A function is defined by f(x) = x^2+2x+c. Find the value of the constant c for which the range of f is given by f(x)≥ 3
    You could convert it to turning point form:

    f(x)=(x+1)^2-1+c

    Then you can see that -1+c must equal 3, so c must equal 4
    Last edited by Stroodle; January 18th 2010 at 01:05 AM. Reason: Made an error
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    So this is using the completing the square method
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    Quote Originally Posted by Stroodle View Post
    You could convert it to turning point form:

    f(x)=(x+1)^2-1+c

    Then you can see that -1+c must be \geq 3, so c must be \geq 4
    I have a question, the question states that, find the values of the constant c.

    now we have an inequality so c can be anything more than 4, how do i answer the question? anything more than 4 or equals to 4 is right?
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    Quote Originally Posted by Punch View Post
    I have a question, the question states that, find the values of the constant c.

    now we have an inequality so c can be anything more than 4, how do i answer the question? anything more than 4 or equals to 4 is right?
    The range is [3, +oo) if c = 4.
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    Quote Originally Posted by mr fantastic View Post
    The range is [3, +oo) if c = 4.
    Sorry but I didn't get you. If you don't understand my question, this was what i was asking, since c is found to be more than or equals to 4, what should i answer the question "find the value of the constant c"?
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    Senior Member Stroodle's Avatar
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    Sorry Punch, I made an error (I'll fix it now). As Mr Fantastic stated the answer is c=4.
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  8. #8
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    Quote Originally Posted by Punch View Post
    Sorry but I didn't get you. If you don't understand my question, this was what i was asking, since c is found to be more than or equals to 4, what should i answer the question "find the value of the constant c"?
    The answer to the question you posted is c = 4, not c \geq 4. That is what my previous reply said. Stroodle made a small misunderstanding of the question: It is required that -1 + c = 3. This misunderstanding should have been clear to you given everything else said in that reply.
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