Which Form To Use?

Question

Quadratic expressions in different forms can be used to describe the same function.  Here are three ways to define function f:

1. Standard Form
2. Factored Form
3. Vertex Form

Which form would you use if you want to find the following features for the graph of f?  Explain your reasoning using complete sentences and/or mathematics.

1. the Zeros (aka x-intercepts)
2. the Vertex
3. the y-Intercept

Answer 1

USE FACTORED FORM To find the Zeros, solutions, or X-intercepts

y = (C1 x + k1)( C2 x+ k2)

the zeros are -k1/C1 and -k2/C2

USE VERTEX FORM to find the VERTEX

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

the vertex is (h,k)

USE STANDARD FORM TO find the y-intercept

y = ax^2+bx+c

the y-intercept is (0,C)