Question

Given the function f(x)= -(x-3)^2+5 how do you find five other exact order pairs?

Answer 1

It is a parabola and the vertex is (3,5)
It has a negative in front of the x^2 term so it is concave downward.
You can plug in two x values to the right of 3, that is 4 and 5. Find the y values that go with those x values. Then you will know the y value for 2 and 1 because parabolas are symmetrical.

Answer 2

Could you give me an example please?

Answer 3

I don't know what you mean? I just gave you an example. The vertex is (3,5) That is 1 point.
Plug 4 in for x. What do you get for y?

Answer 4

Oh!!!!! I get it now! sorry that took me a while....... Thank you!

Answer 5

What did you get for y when you plugged in 4?

Answer 6

I'm solving it right now. Give me a sec

Answer 7

okay. I got -8 is that correct?

Answer 8

f(x)=-(4-3)^2+5
f(x) =-(1)^2+5
f(x)=-1+5
f(x)=4
So the ordered pair is (4,4)

Answer 9

Now parabolas are symmetrical so if (4,4) is on the graph and that is 1 space to the right of the vertex, there must be a corresponding point 1 space to the left of the vertex. Since the vertex is (3,5) that point would by (2,4)

Answer 10

oops. I didn't do the parenthese first.

Answer 11

Now plug in 5

Answer 12

ok

Answer 13

I got 1

Answer 14

Yes. So our 4th point is (5,1) What is the corresponding point 2 units to the left of the vertex?

Answer 15

(4,0)??????

Answer 16

The vertex is (3,5)
One space left of the vertex is (2, )
Two spaces left of the vertex is (1, )

Answer 17

Thus the y coordinates for x=2 and x=4 will be the same because they are both 1 unit from the vertex
The y coordinates for x = 1 and x = 5 will be the same since they are both 2 units from the vertex
The y coordinates for x = 0 and x = 6 will be the same since they are both 3 units from the vertex

Answer 18

This picture might help you understand.
http://www.wolframalpha.com/input/?i=plot%3A+f%28x%29%3D+-%28x-3%29^2%2B5

Answer 19

Quick question. When you told me to plug in 4 for x and then the answer was (4,4) how did you change that to (2,4) if you're moving 1 space to the left of the vertex?

Answer 20

The x coordinate of the vertex is 3 so (3+1,4) is on the graph and (3-1,4) is on the graph

Answer 21

oh so (2,4) is one of the five ordered pairs?

Answer 22

Yes

Answer 23

But (4,4) is not one of the five points correct?

Answer 24

The 5 points are:
1. The vertex (3,5)
2. (3+1,4)
3. (3-1,4)
4. (3+2,1)
5. (3-2,1)

Answer 25

Will it always be like that in other parabola functions? like add 1 subtract 1 and add 2 subtract 2?

Answer 26

That is the easiest way to find additional points.
Find the vertex and then you will only have to calculate 2 more points because you can use the symmetry thing.

Answer 27

Okay. One more question. The 4 and the 5 that you told me to plug in for the x, were they just random numbers?

Answer 28

What is the vertex in your problem?

Answer 29

(3,5)

Answer 30

What is the x coordinate?

Answer 31

3

Answer 32

So do you really think I just chose 4 and 5 randomly or could it have something to do with their proximity to 3?

Answer 33

you chose numbers that were close to 3.........

Answer 34

So if you have another problem someday and the vertex is (-6,7) what x values would it be sensible to choose to get additional points?

Answer 35

-5 and -4

Answer 36

By jove I believe you have it!!!

Answer 37

That's it?????

Answer 38

yep

Answer 39

Oh my gosh! I'm so sorry. It took me a while to put everything together. Thank you so much for being patient with me.

Answer 40

yw.