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Some help on these practice questions and how they are solved would be much appreciated. Ran into some problems in Precalc.

1) Write the complex number in standard form. $6 − \sqrt{-50}$

2) Perform the subtraction and write the result in standard form. $(8 + \sqrt{−48}) − (1 + 4\sqrt{3}i)$

3) Write the complex conjugate of the complex number. $9 − 4i$

4) Find all the rational zeros of the function.

$$f(x) = x^3 – 19x – 30$$

5) Write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point. Vertex: $(3, −1)$; point: $(6, 26)$

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also this one please. Write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point. Vertex: (3, −1); point: (6, 26) –  Kevin Wan May 29 '12 at 3:18
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Please edit your question and add it, don't bury it in the comments! –  Arturo Magidin May 29 '12 at 3:19
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Can you not do any of these? Do you know what "complex conjugate" means, for example? –  Gerry Myerson May 29 '12 at 3:22
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Don't you think that that $4\sqrt{3i}$, which the OP wrote as 4root3i, should be $4\sqrt3i$ instead? From the level of the questions, I doubt his class has found out yet how to calculate $\sqrt{3i}$. Also, question #2 has a particularly simple answer if this is the case. –  MJD May 29 '12 at 3:25
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@Kevin: From the other question I know you don't yet have the textbook, and perhaps haven't yet gotten caught up on class notes from classes you missed. In the meantime, there are several online resources for quick reference that you could use, which might be much more efficient than asking just for help with specific practice problems when you don't know what the practice problems are even asking. For example, googling complex conjugate leads you to sites with the definition and examples. See also en.wikibooks.org/wiki/High_School_Mathematics_Extensions/… –  Jonas Meyer May 29 '12 at 3:34
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1 Answer 1

You should be able to solve #1 and #2 from the advice you got on your other question. If not, say what part you are having trouble with.

For #3, you need to know that the "complex conjugate" of a complex number $a+bi$ is just $a-bi$. The Wikipedia article would have told you this in the first paragraph.

For #4 you should look up the rational root theorem, which allows you to find all the rational roots of a polynomial like the one you have.

Question #5 is ill-posed, since the parabola that is asked for is not unique. Probably the teacher wants you to find a parabola of the form $y = ax^2 + bx + c$. The vertex of such a parabola has its $x$-coordinate at the point where $2ax + b = 0$. Does this help?

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