# Thread: Find the Formula Associated with Each parabola

1. ## Find the Formula Associated with Each parabola

the question is:

part of a roller coaster is modeled by three parabola - some parts removed to give the diagram below.
The first parabola from the left meets the second at co-ordinates (7, 14). using this information from the diagram how can i find the formula associated with each parabola and also workout their relevant domains? hint: think of the 3rd parabola is a translation of the first.

could someone explain in steps if possible how the formulaes and the domains be obtained?

2. ## Re: Find the Formula Associated with Each parabola

To find the equation of a parabola passing through three given points, substitute the points' coordinates (x, y) into the equation y = ax^2 + bx + c. For each point (x, y) you'll get an equation on a, b and c. Then solve this system of three equations to find a, b, c.

3. ## Re: Find the Formula Associated with Each parabola

vertex form equation of a quadratic ...

$\displaystyle y = a(x-h)^2 + k$

where $\displaystyle (h,k)$ is the vertex, and the value of the constant $\displaystyle a$ can be determined by substituting any other point $\displaystyle (x,y)$ that lies on the parabola.

4. ## Re: Find the Formula Associated with Each parabola

Originally Posted by emakarov
To find the equation of a parabola passing through three given points, substitute the points' coordinates (x, y) into the equation y = ax^2 + bx + c. For each point (x, y) you'll get an equation on a, b and c. Then solve this system of three equations to find a, b, c.
max(4.5, 20.25)-->y=ax^2+bx+c-->a(4.5)^2+b(4.5)+c
-->20.25a+4.5b+c=14
min(12, 1.5)-->y=ax^2+bx+c-->a(12)^2+b(12)+c
-->144a+12b+c=1.5
max(19.5, 20.25)-->=ax^2+bx+c-->a(19.5)^2+b(19.5)+…
-->380.25a+19.5b+c=20.25
is this correct? what am i meant to do with the co-ordinates (7, 14)? and how do i proceed from this step to obtain not just the formula but ALSO the relevant domains?