This week in math, we learned how there are three different forms or formulas for quadratic functions. Each one helps us discover an important part about the function and how to graph it.

1) $latex{y=ax^2 +bx + c$}$

General form

This equation easily gives us the y-intercept, as c = the y intercept.

For example if the equation was , we know the y intercept: (0,8)

2) 

Standard/vertex form

This equation gives us the vertex, with p = the x coordinate (the opposite) and q = the y coordinate in the vertex. V: (p,q).

Also, a = the stretch or compression of the function. and  When there is a stretch, it means the parabola will become narrower, and if there is a compression it will become wider. If a = 1, it is neither a stretch or compression, meaning the function is congruent to

For example, if we have the function , we know that the Vertex = (3,3). We also know that it is a stretch of 2.5.

In order to achieve this equation, we complete the square of the general form equation.

3)  y=a(x-x₁)(x-x₂)

Factored form

With this equation, we can find the 2 x-intercepts. x1 and x2 = x-intercepts.

For example, if we have the equation $latex y=2(x-7)(x-1), we know that the x-intercepts are x= 7 and x=1

To achieve this form, you need to factor the general form equation.