# Thread: Maths - Parabola Equations

1. ## Maths - Parabola Equations

Hey guys! I'm new here & browse more thanb I post
I have an emergency, and a lot of guys who are here are pretty knowledgable.
If you could help me out with my question below I would be so happy! Thanks in advance,
Damien.

Question:
I need the EQUATION of a PARABOLA in the form of y = ax^2 + bx + c
I have three points; A (17, 3), B (51,3) and C (34, z)
Z is unkown, however, point C is a local minimum.
So y' = 2ax + b
I need the EQUATION of a PARABOLA in the form of y = ax^2 + bx + c
I have three points; A (17, 3), B (51,3) and C (34, z)
Z is unkown, however, point C is a local minimum.
So y' = 2ax + b. Can anyone help me find the equation of the parabola and the value of z?

2. Originally Posted by damien275x
Hey guys! I'm new here & browse more thanb I post
I have an emergency, and a lot of guys who are here are pretty knowledgable.
If you could help me out with my question below I would be so happy! Thanks in advance,
Damien.

Question:
I need the EQUATION of a PARABOLA in the form of y = ax^2 + bx + c
I have three points; A (17, 3), B (51,3) and C (34, z)
Z is unkown, however, point C is a local minimum.
So y' = 2ax + b
I need the EQUATION of a PARABOLA in the form of y = ax^2 + bx + c
I have three points; A (17, 3), B (51,3) and C (34, z)
Z is unkown, however, point C is a local minimum.
So y' = 2ax + b. Can anyone help me find the equation of the parabola and the value of z?
Given the three points and you know that they lie on a parabola you can write:
$\displaystyle 3 = a \cdot (17)^2 + b \cdot 17 + c$
$\displaystyle 3 = a \cdot (51)^2 + b \cdot 51 + c$
$\displaystyle z = a \cdot (34)^2 + b \cdot 34 + c$

You know that C is a local minimum so from the derivative equation you get
$\displaystyle 0 = 2a \cdot 34 + b$

That's 4 equations in 4 unknowns.

-Dan

3. Please don't create identical threads. Look, you stole topsquark's time. The same thread is here http://www.mathhelpforum.com/math-he...equations.html