# Thread: Equation of a porabola

1. ## Equation of a porabola

Hi I was hoping someone could help me with a math problem I am confused about. If you could, please use simple steps. Thank you

Here is what the problem looks like:

The graph of a parabola passes through the three points (0,3), (1,2), (2,3). Find the values of a, b, c and write the equation of the parabola in the form y = ax^2 + bx +c.

2. Originally Posted by Troy S
Hi I was hoping someone could help me with a math problem I am confused about. If you could, please use simple steps. Thank you

Here is what the problem looks like:

The graph of a parabola passes through the three points (0,3), (1,2), (2,3). Find the values of a, b, c and write the equation of the parabola in the form y = ax^2 + bx +c.
This is a simultaneous equations problem. You will get three equations and three unknowns. Here's how:

For (0,3) => x = 0, y = 3
so y = ax^2 + bx + c becomes
3 = a(0)^2 + b(0) + c
=> c = 3
ah, so we found c from the first, yah! This means we will only need to solve 2 equations. This will turn out easier than i thought.

For (1,2) => x = 1, y = 2
so y = ax^2 + bx + c becomes
2 = a(1)^2 + b(1) + c .........remember, c=3
=> 2 = a + b + 3
=> a + b = -1 ...........(1)

For (2,3) => x = 2, y = 3
so y = ax^2 + bx + c becomes
3 = a(2)^2 + b(2) + c .........remember, c = 3
=> 3 = 4a + 2b + 3
=> 4a + 2b = 0 ..............(2)

So we found c, to find a and b we need to solve the system:
a + b = -1 ................(1)
4a + 2b = 0 ..............(2)

=> 2a + b = 0 ...............(2)/2
......a + b = -1 ..............(1)
=> a = 1

but a + b = -1
=> 1 + b = -1
=> b = -2

so our parabola is:
y = x^2 - 2x + 3

3. y = a(x - p)^2 + q
= a(x - 1)^2 + 2 [Take the turning point of the parabola and insert it into the p and q values]

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

Set (2;3) in the equation. x = 2 ; y = 3

3 = a((2^2) - (2 x 2) + 1) + 2
3 = a(1) + 2
3 = a + 2
a = 1

Thus y = x^2 - 2x + 3

Hope this helps.

4. If i might give you a tip, physically draw the parabola when you are given info like this. It really helps you to understand it and you will see the bigger picture

5. Thank you, both of you.

### application of porabola

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