Quadratics

Finding an Equation (Vertex Form)

 

Throughout this section, we will be looking at deriving equations in vertex form. Please take a look at the video explaining the mathematical procedures to derive an equation in vertex form:

 

 

                                                               Video: Deriving Equations In Vertex Form 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample Problem: Find an equation for the parabola with a vertex (3,-1) that passes through point (1,7).

 

Substitute x=1, y=7, h=3, and k=(-1) into the vertex form equation.

 

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

7 = a(1-3)^2 - 1

7 = a(-2)^2 - 1

7 = 4a - 1

7 + 1 = 4a - 1 + 1

8/4 = 4a/4

a = 2

 

Therefore, the equation is y = 2(x-3)^2 - 1.