Question

.Compare the functions below:


f(x) = 2x2 + 3x − 4 g(x)

trig graph with points at 0, 0 and pi over 2, 3 and pi, 0 and 3 pi over 2, negative 3 h(x)

x y
−3 −8
−2 −6
−1 −4
0 −2
1 0
2 2
3 4


Which function has the largest y-intercept?
f(x)

g(x)

h(x)

All three functions have the same y-intercept.

Answer 1

OK, let me get this straight:

Answer 2

f(x) = 2x^2 + 3x - 4

Answer 3

g(x) is a trig graph with points (0,0), (pi/2, 3), (pi,0), and (3pi/2, -3)

Answer 4

h(x) is the table of x and y values

Answer 5

Yeah c:

Answer 6

OK, now to think...

Answer 7

Well, how can we find the y-intercept? When does this happen?

Answer 8

When it crosses the y-axis?

Answer 9

That is right! Is there a certain value of x = ? that the graph is guaranteed to cross the y-axis?

Answer 10

On the h(x) table?

Answer 11

Well, let's go ahead and look at the h(x) table first.

Answer 12

Any ideas which of those could be the y-intercept?

Answer 13

3?

Answer 14

Like when x=3, y=4?

Answer 15

That is true, but is x = 3 where the graph crosses the y-axis?

Answer 16

Oh Wait, thats not right. It would be -2. Because when x=0, y=-2.

Answer 17

Exactly! Nice!

Answer 18

OK, so we know that h(x) has a y-intercept -2, now we just need to figure out f(x) and g(x).

Answer 19

Maybe f(x). Because g(x) has a y-int of 0.

Answer 20

Perfect, I like it! :)

Answer 21

So, f(x)? ;o

Answer 22

Well, what is the y-intercept of f(x)?

Answer 23

i dont have a clue. o-o. i dont know how to find it.

Answer 24

OK, well, what is special about the value of x = ? when you have a y-intercept? In other words, can you tell me what x equals when the graph crosses the y-axis?

Answer 25

Any graph just like h(x) and g(x) what was special about their x-values when we found the y-intercept?

Answer 26

they were 0.

Answer 27

Yes, exactly! So, it seems like if x = 0, then we will get the y-intercept. Can you use this fact to figure out f(x)'s y-intercept?

Answer 28

SOO. I plug 0 in for x?

Answer 29

Yes! That's it!

Answer 30

OH. Its g(x) ;o

Answer 31

AHA! You've found it! :D

Answer 32

YAAAAY ;D

Answer 33

Congrats! It's a great feeling to solve it!