Question

I'll love you and give you a firm handshake and a medal if you help me. If the points in the table lie on a parabola, write the equation whose graph is the parabola.
|x|-1 | 1 | 3 | 5|
|y|-15|13|-15|-99|
y=

Answer 1

well are you using any software to complete this question.../

Answer 2

The equation for a parabola is:

y = ax^2 + bx + c

One way to do this is to set up 3 occurrences of the above equation, each one with a substitution of "x" and "y" coordinates from your table. What you will then have is 3 equations in 3 unknowns. This is a solvable linear system, best done with Gaussian elimination.

Answer 3

I just plotted the points in geogebra and used a function thats fits a polynomial.

and I'd suggest that it is extremely difficult to determine the equation.

most obvious thing from the data is the parabola is concave down.

Answer 4

There is another "short-cut" method you could use, given that there is some symmetry in the points you are given. You catch a break here because it looks like you have (because of points (-1, -15) and (3, -15)) a vertex at (1, 13) and you can use the general form (vertex form) of the parabola for your substitutions. That is actually easier.

Answer 5

I used the "vertex" method and it works wonderfully and very very easily. I'll show you in the next message.

Answer 6

The vertex form of the equation of the parabola is:

y = a(x - h)^2 + k where the vertex is at (h, k)

It looks like your vertex is at (1, 13) so you only have to find one variable, "a", with only one substitution.

Using point (-1, -15) :

-15 = a(-1 - 1)^2 + 13

That gives "a" = -7, so you have the vertex form as:

y = -7(x - 1)^2 + 13

You can rearrange this into standard form. Do you need help with this?

Answer 7

Yes please. I still don't understand

Answer 8

np. But first, can you expand:

(x - 1)^2

You really should try to do that.

Answer 9

(x - 1)^2 = (x - 1)(x - 1)

and

(m - n)(m - n) = m(m - n) - n(m - n)

= m^2 - mn - mn + n^2

= m^2 - 2mn + n^2

That will help you. Now go ahead and try to expand (x - 1)^2

Answer 10

@jmallis this is the part where you contribute to getting the final answer. What do you have so far?

Answer 11

The middle part. Where Using point (-1, -15) :

-15 = a(-1 - 1)^2 + 13

Answer 12

Yes, what about that part?

Answer 13

@jmallis do try to keep focused here. If you do not respond quickly and frequently, I can't help you because I'm not going to just sit and wait. You will leave me no option but to leave and help other people.

Answer 14

Yeah sorry. Why did you use the ones?

Answer 15

Looking at my 4th post, I used the general form (vertex form) of the equation and substituted the actual vertex for (h, k) in that equation. I also used point (-1, -15) for "x" and "y". That's where the substitutions came into play. All that was left at that point is to solve for "a".

Answer 16

Oh ok. I get it now.

Answer 17

Just re-capping: I outlined 2 methods here. The first one will always work if you are given 3 points. The second and easier method will work if you are given points with symmetry (same y value for 2 different x values).

Answer 18

Also, I determined, from that value of "a" and the vertex, the general (vertex) form of the actual equation. You still don't have it in standard form. That is where we left off.

Answer 19

Oh okay.

Answer 20

So, you can either put it in standard form on your own later on, or you can use my hints and helps right now, already given, and I can stay a little while and help you.

Answer 21

I think I got it now.

Answer 22

Ok, well, good luck to you in all your future studies.

Answer 23

Thank-you again