find formula for the parabola.

[sportsstar469]

hey guys i was wondering if you could help me find this answer, this is not a homework question of mine, but i am studying for a terst, and when i get stuck the best way for me to figure out math is to see the answer and the work, so i can see what steps must be done, and what steps i have issed. i am really stuck on this one.

the problem- Find the equation of the parabola passing through the points (1,2)(3,-14)(-1,-6) it says i must show all algebra necessary to find the equatio nalso.

the attempt- i substituted the points into the equation ax^2+bx+c so i get

2=a^2+b+c
-14=9a+3b+c
-6=a^2-b+c

i know i have to solve this by a three system of equations, but im so lost. if someone wouldnt mind can they solve it for me, so i can see how its done? it would a big help for this test coming. thanks!

 

[wjm11]

Find the equation of the parabola passing through the points (1,2)(3,-14)(-1,-6) it says i must show all algebra necessary to find the equatio nalso.

the attempt- i substituted the points into the equation ax^2+bx+c so i get

2=a^2+b+c
-14=9a+3b+c
-6=a^2-b+c

i know i have to solve this by a three system of equations,

Your set-up on the problem is fine. Good job. If I wanted to solve this, I'd just use matrices and plug it into my calculator. However, since you need to show all the algebra, I'd recommend the Gaussian elimination method. Here is a great example and explanation:

http://www.purplemath.com/modules/systlin6.htm

It can be kind of long and tedious, but the steps are simple and straight forward. Hope that helps.

 

[sportsstar469]

im still confused and i have no diea what i am doing. ive been trying this for a while and its 410 am now =(

 

[Deleted member 4993]

hey guys i was wondering if you could help me find this answer, this is not a homework question of mine, but i am studying for a terst, and when i get stuck the best way for me to figure out math is to see the answer and the work, so i can see what steps must be done, and what steps i have issed. i am really stuck on this one.

the problem- Find the equation of the parabola passing through the points (1,2)(3,-14)(-1,-6) it says i must show all algebra necessary to find the equatio nalso.

the attempt- i substituted the points into the equation ax^2+bx+c so i get

2=a^2+b+c
-14=9a+3b+c
-6=a^2-b+c

i know i have to solve this by a three system of equations, but im so lost. if someone wouldnt mind can they solve it for me, so i can see how its done? it would a big help for this test coming. thanks!

+02 = 1a + 1b + 1c....................................(1)

-14 = 9a + 3b + 1c.....................................(2)

-06 = 1a - 1b + 1c......................................(3)

If you subtract (3) from (1) - you get

8 = 2b

b = 4

Knowing 'b' - you would have two unknowns - use it in (2) and (1) to get

-02 = 1a + 1c ...........................................(4)

-26 = 9a + 1c............................................(5)

from (4) and (5) you should be able to solve for 'a' & 'b".

 

[wjm11]

2=a^2+b+c
-14=9a+3b+c
-6=a^2-b+c

You do realize that those "a" terms are NOT squared, don't you? Only the "x" value that is next to them gets squared when setting up the equations.