Solve Quadratic Equations: Calculate Equation of Curve

[matt_crouch]

how do you calculate the equation of a quadratic curve. A straight line curve uses
y-y1=m(x-x1) is i an alteration of this line?
cheers

 

[Mentallic]

Actually there are multiple ways of expressing lines, quadratics etc.

The general form is
$$y=ax^2+bx+c$$ where $$a\neq 0$$
This is efficient because it is translated into the quadratic formula easily.

There is also the vertex form
$$y=a(x-k)^2+q$$
This form quickly gives the vertex (k,q) of the parabola.

etc.

To calculate the equation of a quadratic, you need 3 points minimum. If you know it's a parabola then you will also know it can be expressed in the general form $$y=ax^2+bx+c$$
If one of the points given to you lie on the parabola, then the point satisfies the quadratic. i.e. you can substitute the x and y value of the point into the general form.
Lets say its (2,3)
Then $$3=4a+2b+c$$ which is a linear equation with 3 variables.
Once you do this for all 3 points, you will have 3 equations with 3 variables. Thus, you can solve them simultaneously to find the values of a, b and c.

These values can then be plugged back into the general form to give you your parabola.

 

[HallsofIvy]

Those are the formulas for quadratic functions- whose graphs are parabolas with vertical axis. You can have parabolas at any angle to the axes but then they are not the graphs of functions.