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I have the following question $f(x) = -x^2 + 4x$ when $x = -3$

Should the structure of the equation be as follows:

$$-3^2 + 4 x -3 = -21$$

The issue I'm having is with the double negative in the variable $x$ and in the function formula.

If anyone can help me, be much appreciated.


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up vote 2 down vote accepted

It should be $-(-3)^2+4(-3)$ which is $-9-12 = -21$.

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Thank you and to confirm if x = 3 (positive) the equation would be -(3)^2+4(3) = 3 Thank you very much for your help by the way. – cocacola09 Feb 23 '11 at 19:47

Several comments:

  1. You don't give a question, so I don't know what "question" you have. You wrote down a formula for a function, and a value for $x$, but no question. Is your question "What is the value of $f(x)$ when $x=-3$, if $f(x)=-x^2 + 4x$?" If so, please write out the question explicitly.

  2. Be careful with the signs and the operations. When you write down a bunch of numbers with operations between them, there is a precedence of operations that is universally agreed upon. Some operations have to happen first. For example, if you write $2+3\times 5$, then the convention is that you do the product first, and the sum second, so that $2+3\times 5$ equals $17$ (not $25$). In particular, one does the exponentials first, then the products (including a minus sign, which is really multiplication by $-1$), and sums at the end.

  3. Now: to evaluate $f(x)$ at $x=-3$, you have to take the formula for $f(x)$, and plug in the value of $x$. That is, take the formula for $f$, which is $$f(x) = -x^2 + 4x$$ and wherever you see an $x$, you have to put in $-3$ instead. Putting parentheses so that it is clear what we are doing, you would have $$f(-3) = -(-3)^2 + 4(-3).$$ When you evaluate this expression, the first thing you need to do is the square. Then you have to do the products (the $-$ times the $(-3)^2$, and the $4$ times $(-3)$); and finally you do the sum of the two totals you have.

    Your attempt is incorrect in sundry ways: you should not have an $x$ left after evaluating; the end result must be a number. You plugged in $3$ for $x$ in the $x^2$ instead of $-3$. And what you wrote, $-3^2+4x-3$, is not equal to $-21$.

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thank you, I've noted my mistakes. – cocacola09 Feb 23 '11 at 19:57

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