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Mathematics 15 Online
Nicole:

http://prntscr.com/l5h9r7

Nicole:

@Vocaloid

Vocaloid:

hint - which choice has a coefficient with a greater absolute value than 1/2?

Nicole:

C?

Vocaloid:

good so C is your solution

Nicole:

http://prntscr.com/l5hacx

Vocaloid:

this is kind of tedious but first you'd have to find the rate of change between each y value, then on top of that, calculate the rate of change of the rate of change (this is easier to show through an example so I'll start with the first choice)

Vocaloid:

-2 --> 24 -1 --> 2 0 --> -1 1 --> 2 2 --> 24 between the y-values, let's calculate the rate of change going from 24 to 2 is clearly a reduction by 22, so we write -22 as the first change then from 2 to -1 is a reduction by 3, so -3 repeating this process we get +3 and + 22

Vocaloid:

now, we put those new changes in a new list, and repeat the process -22, -3, +3, +22 between -22 and -3 that's an increase of 18 between -3 and 3 that's an increase of 6 since the rate of change is not constant (18 and 6 are different) we can conclude this is not quadratic, so we'd move on to one of the other choices

Vocaloid:

B is most likely not quadratic just by visual inspection so move on to choice C

Nicole:

LOL okay

Vocaloid:

try testing choice C using the same process and lmk if you're getting stuck

Nicole:

1 --> -1 2 --> 4 0 --> -4 -1 --> -7 -2 --> -10 from 4 to -1 is 5 from -7 to -4 is -2

Vocaloid:

hm. i'm getting something weird for choices C and D, let me think about this a little more.

Nicole:

okay

Nicole:

its timed so can we go a little faster loll

Vocaloid:

is there a way to skip this question

Nicole:

sure we can move on

Vocaloid:

oh that's easy, if a is negative just pick the graph(s) that are opening downward and going to negative infinity

Nicole:

b and a

Vocaloid:

|dw:1539386938021:dw| should be these two

Nicole:

ohh okay

Nicole:

http://prntscr.com/l5hfi4

Vocaloid:

it's like the pointed part of the graph |dw:1539386980447:dw|

Nicole:

i think C

Vocaloid:

good

Nicole:

http://prntscr.com/l5hfw1

Nicole:

http://prntscr.com/l5hg5t

Vocaloid:

so you should look for the graph where the pointed part is at (-1,-9) and it crosses the x-axis at 2 and -4 to save some time it's one of the first two choices

Nicole:

A

Vocaloid:

good

Nicole:

http://prntscr.com/l5hg9r

Vocaloid:

so the formula of the vertex is -b/2a since b = -6 and a is 3 you get -(-6)/2(3), so first and third only

Nicole:

got it

Nicole:

http://prntscr.com/l5hgwq

Vocaloid:

first step is just plugging in x = 3/4 which would be the first one

Nicole:

http://prntscr.com/l5hhs2

Vocaloid:

length is x, since there are 2 length sides he uses up 2x out of the 100 meters so the width must be whatever's left, 100 - 2x area = length * width = x(100-2x)

Nicole:

http://prntscr.com/l5hi27

Vocaloid:

so basically use -b/2a to find the x-coordinate, then plug it back into the equation to find the y-coordinate x^2 - 6x + 4, b = -6 and a = 1 so -b/2a = -(-6)/2 = 3, then plug 3 back into x^2 - 6x + 4 to find the y-coordinate and see which table has the result

Nicole:

where do we plug the 3

Vocaloid:

x = 3, plug this into x^2 - 6x + 4 to get the y-coordinate

Nicole:

y is (0,13)

Vocaloid:

hm not quite, x = 3 gives us x^2 - 6x + 4 ---> 3^2 - 6(3) + 4 = 9 - 18 + 4 = -5 so (3,-5) making choice B the only viable solution

Nicole:

and do u have a guess for the question we skipped?

Vocaloid:

B maybe? :S

Nicole:

i was thinking a idk

Vocaloid:

I tried asking someone else but they haven't replied yet

Vocaloid:

A might be better idk

Nicole:

A was correct thank you ! LOL

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