Question

The system of equations graphed below will have _____ positive solutions.


Enter the number that correctly fills in the blank in the previous sentence.

Answer 1

http://assets.openstudy.com/updates/attachments/55b835c6e4b0f0c1f1400c5b-itzjustkenya-1438135896974-3858991.png

Answer 2

A solution is visually represented by the point of intersection between the two curves

There are 6 intersection points, so 6 solutions. However, ALL of the intersection points have x coordinates that are negative. Notice how everything is to the left of the vertical y axis. This means that they are considered `negative solutions` and they are NOT positive solutions

So there are 0 positive solutions

Answer 3

The two curves would have to intersect on the right side of the y axis for a positive solution to occur.

Answer 4

wow ok thank you. I have a similar question using the same graph and I already think my answer is correct but I just want to make sure with you if thats ok with you :)

Answer 5

sure go ahead

Answer 6

The system of equations graphed below appears to have _____ solutions.


Enter your answer as the number that correctly fills in the blank in the previous sentence.

Answer 7

so the answer for this would be 6 correct?

Answer 8

using the same graph of course

Answer 9

yes if you drop the `positive` term from the sentence, then there are 6 solutions overall

Answer 10

GOD BLESS YOUR SOUL THANK YOU SO MUCH

Answer 11

would you mind answering just one more question..? I'm very confused..

Answer 12

sure go ahead

Answer 13

All four functions below are quadratic functions. Which function has the greatest maximum value?

Answer 14

y= -(x-10)^2-4

Answer 15

it only gives you one function?

Answer 16

no sorry I'm trying to attach the other options give me like 1 min

Answer 17

y= -x^2-6x-17

Answer 18

those are the 4 options

Answer 19

oh gotcha

Answer 20

y= -(x-10)^2-4 is in the form y = a(x-h)^2 + k

where

a = -1
h = 10
k = -4

do you agree?

Answer 21

correct

Answer 22

the value of k will determine either the min value of y or the max value of y

if a > 0, then k will be the min
if a < 0, then k will be the max

a = -1 means a < 0, so k = -4 is the max of y= -(x-10)^2-4

the largest that y can get is -4

Answer 23

make sense?

Answer 24

yes. slowly but surely following

Answer 25

So write this down: the max of choice A is -4. We'll come back to this later

Answer 26

looking at this graph

http://assets.openstudy.com/updates/attachments/57a512bde4b035cb2d6aef9c-maggy14145-1470436674415-stup.png

where is the peak located? What is the highest point?

Answer 27

16, correct..?

Answer 28

it's located at (1,16)

(x,y) coordinates help you figure out location

the y value is 16, so the max is 16

Answer 29

choice A) The max is -4
choice B) The max is 16

so far, B is winning the race

Answer 30

ok I see that

Answer 31

Look at choice C

http://assets.openstudy.com/updates/attachments/57a512bde4b035cb2d6aef9c-maggy14145-1470436696490-stup2.png

what's the largest y value shown?

Answer 32

19

Answer 33

so the answer to this question would be the 3rd option since the last option's y-value is -17, correct?

Answer 34

and 19 is considered the highest y-value out of options

Answer 35

`since the last option's y-value is -17, correct?`
no -17 is not the max for choice D

Answer 36

y= -x^2-6x-17
is the same as
y= -1x^2-6x-17


y= -1x^2-6x-17
is in the form
y = ax^2+bx+c

where...
a = -1
b = -6
c = -17

The values of 'a' and 'b' will be plugged into `x = -b/(2a)`

what do you get when you do this?

Answer 37

-3

Answer 38

now plug x = -3 back into y= -x^2-6x-17 to get


y= -x^2-6x-17

y= -(-3)^2-6(-3)-17 ... replace every x with -3

y = -(9) - 6(-3) - 17

y = -9 + 18 - 17

y = ???

Answer 39

-8

Answer 40

so the correct answer would be the third option since the rest of the maximum values of the other options were less than the 3rd option right?

Answer 41

so the max of choice D is -8

Answer 42

yes correct

Answer 43

now I should point out that the max of choice C is NOT 19. It's actually something larger. However, we don't need to find the actual max value. We have this summary

Max of choice A is -4
Max of choice B is 16
Max of choice C is some value larger than 19
Max of choice D is -8

so even without knowing the actual max of choice C, we can see that it is the largest max

Answer 44

Thank you so much for helping me! I really appreciate it :)

Answer 45

Glad to be of help