Question

Medal to helper! Can you please check my answers? Important! 5Q's. Thanks!

Answer 1

1. What is the slope of the line which passes through (−2, 0) and (0, 4)?
A. −2
B. 0
C. 2 <--- My Answer
D. Undefined

Answer 2

2. Use the table below to answer this question:
x y
−1 7
3 3
5 1
Find the average rate of change for the given function from x = −1 to x = 5.
A. −6
B. −1 <--- My Answer
C. 1
D. 6

Answer 3

3. What is the equation in point−slope form of the line passing through (0, 6) and (1, 3)?
A. (y − 3) = −3(x − 1) <--- My Answer
B. (y + 3) = 3(x + 1)
C. (y + 3) = −3(x + 1)
D. (y − 3) = 3(x + 6)

Answer 4

4. What is the equation of the graph below?
A. y = − (x + 2)^2 + 2
B. y = − (x − 3)^2 + 2
C. y = (x − 2)^2 + 2
D. y = (x + 3)^2 + 2 <--- My Answer

Answer 5

5. Simplify (x − 4)(x^2 + 3x + 2).
A. x^3 − x^2 + 14x − 8
B. x^3 + 7x^2 − 10x − 8
C. x^3 − x^2 − 10x − 8
D. x^3 + 7x^2 + 14x − 8 <--- My Answer

Answer 6

@phi @Hero @SolomonZelman @tom982

Answer 7

#1 Correct
#2 Correct
#3 Wrong
#4 Wrong
#5 Wrong

Answer 8

No, #3 might be right, let me check again

Answer 9

(0, 6) and (1, 3)
slope=m=(6-3)/(0-1)=3/(-1)=-3

So, with slope -3 and point (1,3) you have:
y - 3 = -3•(x-1)

So #3 is correct.

Alternatively, you could have used the other point (0,6)
y - 6 = -3•(x-0)
y - 6 = -3x

Answer 10

yes, #3 is correct, but #4 and #5 are for sure wrong.

Answer 11

Okay thanks. Could you help me with those two?

Answer 12

Yes, surely.

the general form of the equation of the parabola with vertex at (h,k) is:
\(\large\color{#000000 }{ \displaystyle y=a(x-h)^2+k }\)

If the parabola opens up, a>0
if the parabola opens down, a<0

Answer 13

So, your coefficient must be negative, because the parabola opens down.

Answer 14

And, tell me where is the center of your parabola located?

Answer 15

I mean the vertex, not the center

Answer 16

(3,2)

Answer 17

Yes, that is right.

Answer 18

So, y = − (x − 3)^2 + 2 is correct, right?

Answer 19

\(\large\color{#000000 }{ \displaystyle y=a(x-h)^2+k }\)

h=3
k=2

\(\large\color{#000000 }{ \displaystyle y=a(x-3)^2+2 }\)

So the closes option is
\(\large\color{#000000 }{ \displaystyle y=-(x-3)^2+2 }\)

Answer 20

Alright thank you. Now number 5.

Answer 21

If you want, also, you can solve for "a", and get the answer without eliminating the rest of the options.

Want to solve for a, or to proceed to #5 right away?

Answer 22

I would like to move on to #5.

Answer 23

Alright ...

Answer 24

You have to expand:
\(\large\color{#000000 }{ \displaystyle (x-4)(x^2+3x+2) }\)

Answer 25

Can you tell me what do you get if you were to expand
\(\large\color{#000000 }{ \displaystyle (x-4)\cdot x^2 }\)

Answer 26

You can use the following rules
\(\large\color{#000000 }{ \displaystyle (a+b)\times c=(a\times c)+ (b\times c) }\)
\(\large\color{#000000 }{ \displaystyle (a-b)\times c=(a\times c)- (b\times c) }\)

Answer 27

multiply x^2 and x, then multiply x^2 and -4?

Answer 28

yes, and wha do you get after doing this?

Answer 29

x^3 - 4x^2

Answer 30

yes, very good

Answer 31

Now, what do you get after expanding
\(\large\color{#000000 }{ \displaystyle (x-4)\times 3x }\)

Answer 32

3x^2 - 12x

Answer 33

Yes, very good

Answer 34

And lastly what do you get after expanding
\(\large\color{#000000 }{ \displaystyle (x-4)\times 2 }\)

Answer 35

2x - 8

Answer 36

Yup, now we will put the peaces together...

Answer 37

We wanted to expand
\(\large\color{#000000 }{ \displaystyle (x-4)(x^2+3x+2) }\)

And this is the same as expanding
\(\large\color{#000000 }{ \displaystyle (x-4)\cdot x^2 }\)
\(\large\color{#000000 }{ \displaystyle (x-4)\cdot3x }\)
\(\large\color{#000000 }{ \displaystyle (x-4)\cdot2 }\)
separately, and then adding the results.

We get that:
\(\large\color{#000000 }{ \displaystyle (x-4)\cdot x^2=\quad +x^3-4x^2 }\)
\(\large\color{#000000 }{ \displaystyle (x-4)\cdot3x=\quad +3x^2-12x }\)
\(\large\color{#000000 }{ \displaystyle (x-4)\cdot2 =~{{\tiny~~}}\quad +2x-8}\)

And add the results:
\(\large\color{#000000 }{ \displaystyle x^3-4x^2+3x^2-12x+2x-8 }\)

Answer 38

Can you simplify
\(\large\color{#000000 }{ \displaystyle x^3-4x^2+3x^2-12x+2x-8 }\)

?

Answer 39

Yes, let me try.

Answer 40

go ahead and take your time ;)

Answer 41

x^3 - x^2 - 10x - 8

Answer 42

yup, and that is your final answer.

Answer 43

Wow. I would have never guessed that one. You're explanation makes sense. Thank you so much!

Answer 44

Could you check this too?:
Which of the following is the conjugate of a complex number with 2 as the real part and −8 as the imaginary part?
A. −2 + 8i
B. 2 + 8i <--- My Answer
C. 2 − 8i
D. −2 − 8i