Question

College Algebra: I'm doing 3X3 Linear Systems and I need help solving this problem. I tried a technique my professor taught me; however, it's not working this time. I need to use a system of equations to find the parabola of the form y=ax^2+bx+c that goes through the three given points:
(0,4) (-2,0) (-3,1)

Answer 1

First, plug the x and y to that equation
So you have 3 equations with 3 variables to solve(A,B, and C)

And would like like to work on it using your professors technique?

Answer 2

When I started plugging them in, I got c=4, 4a-2b+c=0, and 9a-3b+c=1. After that, everything I did didn't make sense

Answer 3

Ok. Everything's right so far.
Can you show me what you did next?

Answer 4

put c=4 ,then you are left with two equations in a and b solve them .

Answer 5

Alright.
Next, I plugged in the 4 where the C took place. So I had 4a-2b+4=0 and 9a-3b+4=1

Answer 6

But of course, I moved it on the other side. So, it was 4a-2b=-4 and 9a-3b=-3

Answer 7

Good.
Now you want to try to elimation one of the variable to solve for the other.

For example ,multiplying both sides of the first equation by 3 and the other by 2 will get rid of b

Answer 8

And you'll be able to solve for what a is

Answer 9

2a-b=-2
3a-b=-1
subtract and get the value of a and then b

Answer 10

So, like this?
\[-3(4a-2b)=(-4)-3\]
\[-2(9a-3b)=(-3)-2\]

Answer 11

Wait, what?

Answer 12

Exactly.
And now multiply it out

Answer 13

Alright, I got -12a+6b=12 and -18a+6b=6

Answer 14

Ok. Now subtract the two equations.
Notice that the b's will cancel out. (6b-6b=0)

And you should be able to solve for a

Answer 15

a=1

Answer 16

Yea. And now you know a=1 and c=4.
Just plug them into any of the equations to find b

Answer 17

Oh cool, Alright. Let's see.

Answer 18

b=4

Answer 19

Correct

Answer 20

Ohhhh. So that's how the answer is y=x^2+4x+4

Answer 21

Thank you so much Nikato. I truly do appreciate your help. :)

Answer 22

Yea. You're welcome.
You were a good learner

Answer 23

Thank you, I have a final exam coming up soon; therefore, I'm trying my best to pass. It's my best hope. :)

Answer 24

Good luck on your exam!

Answer 25

Thank you!!!!