Question

how do i find a if my equation is y=a(x-.5)^2+2

Answer 1

Do you have a known value of x and y?

Answer 2

No. I just have my vertex for h,k which is (0.5,2)

Answer 3

do you know any other points on this parabola?

Answer 4

yes (0.5,2) & (7,2)

Answer 5

your vertex is certainly a point on the parabola, no?

Answer 6

Yes

Answer 7

so plug in the coordinates of a known point and solve for \(a\)

Answer 8

Thats where im confused. The equation in general form is y=a(x-h)^2+k my h,k can either be (7,2) or (0.5,2) so i have now y=a(x-7)^2+2 ?

Answer 9

y=a(x-.5)^2+2

2=a(7-0.5)^2+2 ... plug in (7,2)

2=a(6.5)^2+2

...
...
...

a = ???

Answer 10

A=0.04?

Answer 11

oh wait, are you sure the other point (that's not the vertex) is (7,2) ?

Answer 12

The two points on the paraobla i have is (.5, 2) & (7,2)

Answer 13

then none of those two are the vertex

Answer 14

So what is the h,k then ?

Answer 15

the vertex would be the point (h,k)

where h = (0.5+7)/2 = 7.5/2 = 3.75

but we can't determine the value of k unless we get more info

Answer 16

What else information do i need

Answer 17

another point at least

Answer 18

(9,2)(2.5,2.08)(5.68,5.1)

Answer 19

are you able to post a picture of this at all?

Answer 20

How do i post it?

Answer 21

click attach file

Answer 22

under the text box

Answer 23

Where?

Answer 24

see where it says "draw"?

Answer 25

im on my phone i dont see it

Answer 26

oh, hmm I'm not sure if it's the same on mobile devices

Answer 27

try scrolling down?

Answer 28

I can send the link

Answer 29

ok

Answer 30

Its not letting me , but the picture is on google search real world parabolas And its the sixth picture

Answer 31

all I see is the mcdonalds picture and a bunch of roller coasters...hmm I'm doing something wrong

Answer 32

No its the tower picture after the red roller coaster

Answer 33

so this page

http://mathforum.org/mathimages/index.php/Parabola

???

Answer 34

No go to google image search & type real world parabolas

Answer 35

this is what I get

http://cameronjtesblog.blogspot.com/2011/04/real-world-parabolas.html

Answer 36

so I think I'm on the wrong page (again...)

Answer 37

Go to google.com

Answer 38

ok

Answer 39

then what?

Answer 40

Then type in real world parabolas

Answer 41

ok did that

Answer 42

which # link am I looking for?

Answer 43

There's no link . Its a picture of a tower

Answer 44

yeah getting the same results, are you sure there's no way to send the link?

the direct link

Answer 45

It wont copy right . Im trying

Answer 46

http://www.google.com/search?q=real+world+parabolas&client=ms-android-metropcs-us&hl=en&source=android-search-app&v=141400000&tbm=isch&tbo=u&source=univ&sa=X&ei=wEjSUauTDY3m9gSy24H4Dw&ved=0CCgQsAQ&biw=320&bih=407

Answer 47

thanks

Answer 48

Do you see it

Answer 49

I get the same results that I did if I were to search it myself

I meant the direct link to the actual picture...sorry for being a pain

Answer 50

I think your phone and my computer deliver different results or something, not sure

Answer 51

Its okay hold on.

Answer 52

ok

Answer 53

http://1.bp.blogspot.com/-WzFicpco5wA/TatX8Q8AHQI/AAAAAAAAABw/DPBcSKUQ_dY/s1600/Screen+shot+2011-04-17+at+5.11.48+PM.png

Answer 54

yeah that's what I've been getting...but that has no numbers on it

Answer 55

I'm guessing you're supposed to add in the points later?

Answer 56

yeah i use this geogebra thing & it gives me the points

Answer 57

ah send me that if you can as well, if not, then its ok

Answer 58

basically I was hoping to see this thing for myself to see where the vertex was

Answer 59

Im not close to a computer so i cant

Answer 60

alright then no worries

Answer 61

Okay

Answer 62

I can tell you right off the bat that the vertex will not be on the same horizontal level as any other point that's on the parabola

Answer 63

so there's no way that (0.5, 2) can be the vertex if another point is (7, 2)

Answer 64

So it would be the middle point

Answer 65

yeah at (3.75, k)

Answer 66

But how do i find k

Answer 67

and you also said that (9,2) is on the parabola right?

Answer 68

Yes

Answer 69

that's just not possible

in any parabola, only 2 points will share the same y coordinate (so you can't have 3 points that have a y coordinate of 2)

Answer 70

so this is part of the reason for my confusion and why I wanted to see a pic of the whole thing

Answer 71

I have to make a quadratic formula based of the parabola in the picture & the geogebra gaves me those points

Answer 72

hmm there's probably a typo somewhere then

if we had the 3 points (0,5, 2) (7, 2) and (9,2)

the you would either have a linear equation or a cubic (but not a quadratic) going through those 3 points

Answer 73

so hopefully you see the issue here

Answer 74

no the points are (9,2)(2.5,2.0)(5.68,5.1)

Answer 75

I'm assuming those points are labeled A, B, and C in geogebra right?

Answer 76

Yeah

Answer 77

ok what you can do is with geogebra you can type

"fitpoly[A,B,C,2]"

without quotes into the input bar at the bottom

what this will do is interpolate a polynomial (ie draw a polynomial through all 3 points) and it will force the polynomial to be of degree 2, so it will be a parabola

Answer 78

this saves you a lot of time from doing it by hand (which involves ugly systems of equations and matrices), so that's fortunate you're able to use geogebra

Answer 79

Okay. And then from there what do i do

Answer 80

what equation do you get?

Answer 81

when you type that command into geogebra

Answer 82

I didnt do i just wanted to know so that when i do i wont get stuck

Answer 83

well once you have the equation, you can determine the value of 'a' by looking at the leading coefficient

Answer 84

you can also determine the vertex by typing in

"max[f,-20,20]"

without quotes into the input bar

Answer 85

Okay, & then.from there im asked to find the x & y-intercepts

Answer 86

the y-intercept would be the last number in the function you get from after doing the "fitpoly" command

the x-intercepts can be found by typing


"root[f]"


without quotes into the input bar

Answer 87

Okay thanks

Answer 88

you're welcome