Question

Find the quadratic equation from the following data
The intercepts are (-3,0) and (0,18)

Answer 1

quadratic has the form f(x)=ax^2+bx+c right?

Answer 2

we are given that those two points lie on the quatric so we have f(-3)=a(-3)^2+b(-3)-c=0 and we have f(0)=c=18 so f(-3)=9a-3b-18=0

Answer 3

so we have 9a-3b=18 or 3a-b=6 if we divide both sides by 3

Answer 4

but we have two unknowns so now i'm stuck maybe we should try the form f(x)=a(x-h)^2+k

Answer 5

I don't know much, but if I am correct, the equation must be of the form ay^2+by+c=0

Answer 6

As you see there is only one x intercept

Answer 7

you can use either form

Answer 8

I don't think so, as you see while you use the x form, you are putting the value of x in the equation, and that I think will not work

Answer 9

Though I am not sure

Answer 10

we know the y-intercept which is (0,18) so we have f(x)=a(x-h)^2+18 now we need to find h and a

Answer 11

0=f(-3)=a(0-h)^2+18=ah^2+18 so we have ah^2=-18

Answer 12

so either way we still have two unknowns

Answer 13

oh i see what you are saying no y=f(x) not x=y

Answer 14

Now you got it

Answer 15

its f(x)=ax^2+bx+c or you can use f(x)=a(x-h)^2+k

Answer 16

we don't know anything else about the parabola?

Answer 17

I beg your pardon?

Answer 18

If you find any solution please post it here, I will have to leave now, as there is a black out here

Answer 19

i was just asking if we know anything else about the parabola?

Answer 20

go lokisan!

Answer 21

Iam, I may be able to look at it a bit later. My first impressions of it are to find the slope of the line that joins the two points, use that to perform a rotation back to the x-axis, solve the equation normally and then transform back. Or you could transform the general equation by the same angle and solve straight from the points.

Like I said, this is a cursory glance. I don't have time available at the moment to work through it properly, but I will when I can...promise.

Answer 22

haha, just saw what you wrote, myininaya...

Answer 23

lol .

Answer 24

And I forgot to say, you may want to translate your points to the right 3 units before rotating...so your points would be (-3,0) --> (0,0) and (0,18) --> (3,18).

Hope this is making sense.

Answer 25

ignorant, do we know anything else about the parabola?

Answer 26

like the vertex or something else?

Answer 27

No that is all the information I have about it

Answer 28

can you make sense out what lokisan is saying? it looks like he has a way to find the equation of the parabola

Answer 29

Yes, I can get the idea of what he is saying. And I am trying to work it out on pen and paper.
If you have any more clue, please post it

Answer 30

do you know derivatives?

Answer 31

Yes sure

Answer 32

http://en.wikipedia.org/wiki/Rotation_matrix

Answer 33

ok awesome

Answer 34

f'(x)=2ax+b

Answer 35

Forget the matrix stuff if you haven't done it. You can use the equations.

Answer 36

Actually I happen to have learnt that rotation part of matrix

Answer 37

Good

Answer 38

Your problem is:

(3,18)=R(x,y) where the ( , ) are vectors and R is the rotation matrix.

You need to invert R to find (x,y)=R^{-1}(3,18).

You'll then have two points, (0,0) and (x,0) (since both points will now be on the x-axis).

I'm rushing through this...I've just thought of a 'better' method, but I'm rushed...if I can sort it out later, I will.