# Thread: parabolas and finding variables

1. ## parabolas and finding variables

hey guys, im new to the forum and i need some major help with some stuff

The question is asking me to find a and k so that a parabola y = ax^2 +k passes through the points:

(-3, 11) and (4, 18)

can somebody please teach me how to find the 2 variables a and k?

Mike

2. Originally Posted by imppy725
hey guys, im new to the forum and i need some major help with some stuff

The question is asking me to find a and k so that a parabola y = ax^2 +k passes through the points:

(-3, 11) and (4, 18)

can somebody please teach me how to find the 2 variables a and k?

Mike
This is a simultaneous equations problem.

we are given y = ax^2 + k and we are given two sets of values for x and y, that is, (x,y) = (-3,11) and (x,y) = (4, 18) so now we just plug them in.

If (x,y) = (-3,11)
y = ax^2 + k
=> 11 = a(-3)^2 + k
=> 11 = 9a + k ....................(1)

If (x,y) = (4, 18)
y = ax^2 + k
=> 18 = a(4)^2 + k
=> 18 = 16a + k ...................(2)

so now to find a and k, we just need to solve the system:

9a + k = 11 ................(1)
16a + k = 18 ..............(2)

=> 7a = 7 .........(2) - (1)
=> a = 1

but 9a + k = 11
=> 9(1) + k = 11
=> 9 + k = 11
=> k = 2

so the parabola is y = x^2 + 2

3. Originally Posted by Jhevon
so now to find a and k, we just need to solve the system:

9a + k = 11 ................(1)
16a + k = 18 ..............(2)

=> 7a = 7 .........(2) - (1)
=> a = 1

but 9a + k = 11
=> 9(1) + k = 11
=> 9 + k = 11
=> k = 2

so the parabola is y = x^2 + 2
Thanks for your help, though I only understand what you did up until here. I dont understand how you got from:

9a + k = 11 ................(1)
16a + k = 18 ..............(2)

to

=> 7a = 7 .........(2) - (1)
=> a = 1

do you think you can explain it to me please?

edit: i finally understand what you did there, you used equation 2 to subtract equation 1, but will you explain to me why you have to do that?

thanks, sorry for all the trouble, but i just want to know the reason why i have to do certain things in order to get the answer, I don't want my teacher asking me why to do it, and I don't know how

4. Originally Posted by imppy725
Thanks for your help, though I only understand what you did up until here. I dont understand how you got from:

9a + k = 11 ................(1)
16a + k = 18 ..............(2)

to

=> 7a = 7 .........(2) - (1)
=> a = 1

do you think you can explain it to me please?

edit: i finally understand what you did there, you used equation 2 to subtract equation 1, but will you explain to me why you have to do that?

thanks, sorry for all the trouble, but i just want to know the reason why i have to do certain things in order to get the answer, I don't want my teacher asking me why to do it, and I don't know how
ok, so you realized that i subtracted equation 2 from 1, good. But why? Well, this is a standard method for solving simultaneous equations. solving an equation with one variable is easy, so our objective is to get one variable. so to acheive this, we try to get the coefficient of one of the two variables the same in both equations. Here, the coefficient of k was already the same in both equations, that is 1. Then subtracting the two equations allow me to get rid of k, since 1k - 1k = 0. that way i am left with a only, and solving the equation becomes easy.

after finding a, i can substitute its value into either equation to find k

5. Originally Posted by Jhevon
ok, so you realized that i subtracted equation 2 from 1, good. But why? Well, this is a standard method for solving simultaneous equations. solving an equation with one variable is easy, so our objective is to get one variable. so to acheive this, we try to get the coefficient of one of the two variables the same in both equations. Here, the coefficient of k was already the same in both equations, that is 1. Then subtracting the two equations allow me to get rid of k, since 1k - 1k = 0. that way i am left with a only, and solving the equation becomes easy.

after finding a, i can substitute its value into either equation to find k
alright, great thanks, this helps a lot. =)

Mike

6. Originally Posted by imppy725
alright, great thanks, this helps a lot. =)

Mike
you're welcome