Question

Two functions are shown in the table below.


Function 1 2 3 4 5 6
f(x) = −x2 + 4x + 12
g(x) = x + 8


Complete the table on your own paper, then select the value that is a solution to f(x) = g(x).
A)x = 3
B)x = 4
C)x = 5
D)x = 6

Answer 1

@butterflydreamer @chrisdbest @brebre5564

Answer 2

@CaptainLlama49

Answer 3

@mathmate

Answer 4

Lemme see

Answer 5

OK

Answer 6

its been a while since ive done this lol do you know what f(x) stands for cx

Answer 7

NOP

Answer 8

ARE YOU THERE?

Answer 9

@CaptainLlama49

Answer 10

Sorry lol cant help you there

Answer 11

@Study_together

Answer 12

@ospreytriple

Answer 13

@Kash_TheSmartGuy

Answer 14

Hmm... If I'm reading this right, it looks like they just want you to plug in different x values (from 1 to 6) into the equations.

Answer 15

So, if we started with the "f(x)" equation we are thinking about \[-x^2 + 4x + 12\] and we want to plug in different x values to see what we get. What would you get if you plug in x =1?

Answer 16

the answer its 6?

Answer 17

Well, let's see. What did you do to get that answer?

Answer 18

i calculate: −x2+4x+12

Answer 19

\[f(x) = −x^2 + 4x + 12 \]\[g(x) = x + 8 \]\[f(x)=g(x)\iff -x^2+4x+12=x+8\]

Answer 20

OK, that sounds right. Maybe there was just a calculation error. I did -(1)^2 + 4(1) + 12 = -1 + 4 + 12 = 15. Does that make sense?

Answer 21

yes

Answer 22

OK, so in the "f(x)" row under the "1" column you would fill in 15.

Answer 23

You should have something like this so far

1 2 3 .....
f(x) 15
g(x)

Answer 24

It's a little tedious, but we have to repeat our calculations for all x's up to 6. Next is x = 2. Plug that into -x^2 + 4x + 12 and see what you get. I'll check your answer. :)

Answer 25

i get 6? i dont know if i'm right

Answer 26

OK, can you write your steps like I did before?

Answer 27

ok let me see

Answer 28

sure, take your time. :)

Answer 29

like this?

Answer 30

f(x)=−x2+4x+12
g(x)=x+8
f(x)=g(x)⟺−x2+4x+12=x+8

Answer 31

Well, not exactly. But good job copying all those formulas! :)

I meant when you plug in x = 2 into -x2+4x+12. Like this

-(2)^2 + 4(2) + 12 = ...

What comes next?

Answer 32

so, -(2)^2 = -4 and 4(2) = 8 so we get
-(2)^2 + 4(2) + 12 = -4 + 8 + 12 = ...
could you finish this part?

Answer 33

16?

Answer 34

Yes! Exactly! :D

Answer 35

Good job! That's all I meant by "show your steps". Anyways, we now have the second piece of our table

1 2 3
f(x) 15 16
g(x)

Does this make sense so far?

Answer 36

yes

Answer 37

OK, let's keep going. Next is x = 3. Let's plug this into -x^2 + 4x + 12 and see what we get. I'll help get you started:

-(3)^2 + 4(3) + 12 =

What comes next?

Answer 38

=15?

Answer 39

Good!

Answer 40

so, whats nexts?

Answer 41

Alright, so we still need to do the same thing for x = 4, x = 5, and x = 6. Then we will be done plugging into the -x^2 + 4x + 12 equation. See if you can do these:
-(4)^2 + 4(4) + 12 =
-(5)^2 + 4(5) + 12 =
-(6)^2 + 4(6) + 12 =

Answer 42

yea give a second

Answer 43

Of course, that's a lot of numbers. :)

Answer 44

.12
.7
.0

Answer 45

Very good! You got them all!

Answer 46

OK, phew... almost done. We have finally completed the first row of the table:

1 2 3 4 5 6
f(x) 15 16 15 12 7 0
g(x)

Answer 47

so whats next's?

Answer 48

Next is the easier formula. We do the same thing we did for f(x), but now for g(x).

Plug in x = 1, x = 2, x = 3, x = 4, x = 5, and x = 6 into

x + 8 (that's g(x)).

Answer 49

As long as we don't get freaked out, we can see that this is pretty quick to figure out.
1 + 8 =
2 + 8 =
3 + 8 =
4 + 8 =
5 + 8 =
6 + 8 =

Answer 50

These answers will go into the second row of our table.

Answer 51

ok let me solve

Answer 52

.9
.10
.11
.12
.13
.14

Answer 53

Great job! You've got it!

Answer 54

Let's put these into the table:

1 2 3 4 5 6
f(x) 15 16 15 12 7 0
g(x) 9 10 11 12 13 14

Answer 55

Cool! The table is finished like the problem wanted. Their last question was, when does
f(x) = g(x) ?

We just have to look at the table and see when the two numbers are the same. Which x value seems to have the same number for both f(x) and g(x)?

Answer 56

yea, f(x) and g(x) have the 12

Answer 57

Good! There's the match, so x = ? to make this happen. Our choices are:
A)x = 3
B)x = 4
C)x = 5
D)x = 6

What do you think?

Answer 58

4?

Answer 59

Yep! That's the one! If we weren't sure we could just confirm that
-(4)^2 + 4(4) + 12 = 12
and
4 + 8 = 12
just like we wanted.

Finally! We are done! Congrats!

Answer 60

thank you so much! you explain good! can you help me with 3 more please?

Answer 61

I wish I could, but I've got to go for now, I've got some of my own homework to finish. Sorry. :(

Good luck! I'm sure someone else can help you out. :)

Answer 62

its fine

Answer 63

Have a good night, or morning, or whatever time it is where you are. :)

Answer 64

night