Quadratic Functions and

Graphs

11

12.1 Introduction

EMBAV

In Grade 10, you studied graphs of many different forms. Here you will learn how to sketchand

interpret more general quadratic functions.

See introductory video:VMfkg at http://www.everythingmaths.co.za

11.2 Functions of the Form y = a(x + p)^2 + q

EMBAW

This form of the quadratic function is slightly more complex than the form studied in Grade 10, y =

ax^2 + q. The general shape andposition of the graph ofthe function of the form f(x) = a(x+ p)^2 + q

is shown in Table 11.1.

1

2

3

− 1

− 2

− 3

5 4 − 3 − 2 − − 1 − 1 2 3 4 5

Figure 11.1: Graph of f(x) =^12 (x + 2)^2 − 1

Activity: Functions of the Formy=a(x+p)^2 +q

1. On the same set of axes, plot the following graphs:
   (a) a(x) = (x− 2)^2
   (b) b(x) = (x− 1)^2
   (c) c(x) = x^2