Question

The graph of which quadratic equation is shown below?

a u-shaped graph on a coordinate plane that is opening up and has a vertex of (1, −9)

y = x2 − 2x − 8

y = x2 + 2x − 8

y = −x2 + 2x − 8

y = −x2 − 2x − 8

Answer 1

When you look at the equation of a quadratic function, do you know how to determine if the parabola opens up, or opens down? That lets you eliminate two of these answers.

Answer 2

Then, you COULD just check the point in the other two equations.

Although, the more rigorous method would be to use the vertex for for a quadratic:

y=a(x-h)^2-k

plug in your given h and k, and multiply it out - see which equation you get.

Answer 3

yes i know when a is positive the porabola is opened up but if it is negative it goes down and i also knowthat is the it's opened up it mans it's minimum and down is maximum that is all i know

Answer 4

so that eliminates the two first answerss? @DebbieG

Answer 5

@DebbieG sir are you there?

Answer 6

Sorry, I stepped away from the computer.

and I'm not a sir... lol. :)

You are correct that a>0 means that the parabola opens up, and a<0 means that it opens down.

but why do you think that the first 2 answers are eliminated? You said that your graph opens up... so a has to be....? positive, or negative?

Answer 7

positive and sorry about calling you a sir the photo made me think it was you

Answer 8

LOL I get that a lot. Those are my sons. :)

OK, right - so a has to be positive. So which 2 answers does that rule out?

Answer 9

the two last ones

Answer 10

but in my graph the porabula looks like "u" not an "n" if you know what i'm trying to say

Answer 11

Right - it opens upward. That means a>0. That means that your answer can't be C or D above, because they have a<0, right?

So now you just need to decide if it is A or B.

Answer 12

i'm sorry ma' am but the graph is going down so shouldn't we eliminate the top two (only asking questions to understand)

Answer 13

oh nevermind sorry

Answer 14

lol.. well, yes, that does change things. so it OPENS DOWN? Because above you said that it OPENED UP.

OK, so are we back to it opens up??

Answer 15

if it opens up, it's one of the first 2 equations. If it opens down, it's one of the last 2 equations.

Answer 16

let me send you a picture ma' am

Answer 17

ok

Answer 18

this is what i have

Answer 19

Yes, that opens up.

Answer 20

so a>0

Answer 21

ok

Answer 22

So you have a vertex of (1, −9). Like I said above, there are a few different ways to proceed.

If you knwo the "vertex form" of a parabola, you could use that and plug in the vertex:
(1, −9) to the vertex form y=a(x-h)^2-k.

You know that a=1, so you would just expand the (x-h)^2 and see which equation you get.

Answer 23

so do you want me to find the vertex first?

Answer 24

Or, you could "plug and chug" - trying the vertex in each of those 2 equations. See which graph it is on - if it's only one, then you know that's the one.

I don't prefer that method though, because it is only BECAUSE this is a multiple choice problem that you can do it. it doesn't give you a rigorous understanding of the quadratic.

Answer 25

Hmmm.... well, you HAVE the vertex. You could find the vertex of the equations given in the answer choices, that's another way to go about it.

Answer 26

sorry lost connection but so you want me to plug in the 1 and -9?

Answer 27

Well, I've given you several options. You know that it's one of the first two equations. there are a variety of ways to determine which one. Why don't you tell me what you think would work, and what your result is?

Answer 28

I think we should use plug and chug since we do have the answer choises

Answer 29

so should I plug and chug and tell you what I get? or do you want to do it together ma'am?

Answer 30

i got b ma'am @DebbieG

Answer 31

How did you get that?

Answer 32

i asked my dad

Answer 33

Does \(\large y = x^2 + 2x − 8\) have vertex (1, -9)?

OK, no offense to your dad, but chances are good that you know more about quadratic equations than he does.

Answer 34

Does \(\large y = x^2 + 2x − 8\) have vertex (1, -9)?

Answer 35

Is (1, -9) a point ON THE GRAPH of \(\large y = x^2 + 2x − 8\)?

Answer 36

let me see

Answer 37

i got 1 and -5

Answer 38

You got (1, -5) as the vertex of \(\large y = x^2 + 2x − 8\)? Can you tell me how you got that?

Answer 39

Or are you just saying that you tried x=1, and got that y=-5?

THAT is correct. Which means that (1, -9) is NOT the vertex of this one, right?

Answer 40

(1, -5) is not the vertex either; but it IS a point on the graph.

However, (1, -9) is not even on the graph of this one.

Answer 41

well i did
x = -b/2a and then wrote x = -2/2(1) which is x = -2/2 = x= -1
and then did y = -1^2 + 2(-1) - 8 y = 1 - 2 - 8 y = 9

Answer 42

oh i meant -1 and 9 not 1 and -5 oops

Answer 43

so it is A

Answer 44

because: x = -b/2a
x = 2/2
x = 1
y = 1 - 2 - 8
y = 1-10
y = -9

Answer 45

Ok, there is a big difference between (-1, 9) and (1, -5).... lol.

But in any case, the equation you are looking for has a vertex of (1, -9).

You are correct that the vertex of B has x=-1 (which is enough to rule out B as the answer).

However, you made an error in finding the y coordinate of B:
y = -1^2 + 2(-1) - 8
y = 1 - 2 - 8 <------ right here.... 1-2-8=-9 NOT =9

And YES you are correct - it is A. As your calculations show, THAT one has vertex (1, -9).

Answer 46

ok thank you so much for your help without you i wouldn't have understood the problem or how to solve it and i feel like i learned a lot thank you so much for all your help and effort ma'am! :)