Complex Numbers in Standard Form and other assorted problems

Question

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: $(6, 26)$

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?