Simplify 6/(3-12i), find max/min of f(x)=x^2-10x+29, find range of f(x)=-2x^2-16x-38

[dallasguy90]

I'm on the second week of an eight week course and tomorrow is Exam 2 and I have a few questions from our review:

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#7. Simplify. Write your answers in the form of a + bi, where a and b are real numbers.

. . . . .\(\displaystyle \dfrac{6}{3\, -\, 12i}\)


#23. Determine whether there is a maximum or minimum value for the given function, and find that value.

. . . . .\(\displaystyle f(x)\, =\, x^2\, -\, 10x\, +\, 29\)


#27. Find the range of the given function.

. . . . .\(\displaystyle f(x)\, =\, -2x^2\, -\, 16x\, -\, 38\)

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Please let me know how to solve them, I don't need the answers I just want the steps, I've been struggling or I might be overthinking it. Thank you

 

[tkhunny]

Couple of problems.

1) I can't see any of your work.

2) What's the difference between all the steps and the answer?

3) You appear to be recognizing the pieces of a quadratic equation.

4) You can't just add things to the numerator and denominator and expect it to be the same.

 

[Steven G]

I'm on the second week of an eight week course and tomorrow is Exam 2 and I have a few questions from our review:

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#7. Simplify. Write your answers in the form of a + bi, where a and b are real numbers.

. . . . .\(\displaystyle \dfrac{6}{3\, -\, 12i}\)


#23. Determine whether there is a maximum or minimum value for the given function, and find that value.

. . . . .\(\displaystyle f(x)\, =\, x^2\, -\, 10x\, +\, 29\)


#27. Find the range of the given function.

. . . . .\(\displaystyle f(x)\, =\, -2x^2\, -\, 16x\, -\, 38\)

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Please let me know how to solve them, I don't need the answers I just want the steps, I've been struggling or I might be overthinking it. Thank you

No, we don't do that here. We will help YOU get the answer. Thank you.

7) You want to change the way the fraction looks since you do not want an i in the denominator. WHENEVER you want to change the way something looks you multiply by 1. Understand that there are many ways to write 1 (7/7= 3 ft/1yd, 100%, ...=1)
In your case you need to use the fact that (a+bi)*(a-bi) = a^2 - b^2 so there are no i's

Do this problem, show us your work and if it's correct we will go onto the next problem. ...

 

[HallsofIvy]

Unfortunately a large part of your calculation has been cut off! If you would type your calculations here, that would help a lot!

 

[stapel]

#7. Simplify. Write your answers in the form of a + bi, where a and b are real numbers.

. . . . .\(\displaystyle \dfrac{6}{3\, -\, 12i}\)

What does your book say about "rationalizing denominators" containing complex numbers? (here)

#23. Determine whether there is a maximum or minimum value for the given function, and find that value.

. . . . .\(\displaystyle f(x)\, =\, x^2\, -\, 10x\, +\, 29\)

What have you learned about max/min points of parabolas? Have you learned how to complete the square to convert a quadratic into vertex form?

#27. Find the range of the given function.

. . . . .\(\displaystyle f(x)\, =\, -2x^2\, -\, 16x\, -\, 38\)

What have you learned about max/min points of parabolas? Given that this is a negative quadratic, what sort of parabola will it graph? So will it have a max or a min? At what x-value? Of what y-value? Then what is its range?

If you get stuck, please reply with a clear listing of your thoughts and efforts in response to the questions above. Thank you!