This document discusses properties of quadratic functions and their graphs. It explores expressing quadratic functions in different forms, sketching graphs of basic quadratic functions, and investigating the effects of changing coefficients on the graph. The key aspects covered are the relationship between the coefficients and the graph properties like the vertex, line of symmetry, and y-intercept. Examples of matching functions to graphs and writing functions in standard form are provided.

1. To explore the properties of quadratic functions
and their graphs.
To investigate the different forms in which
quadratic functions can be expressed.
http://www.youtube.com/watch?v=VSUKNxVXE4E&feature=player_embedded#
http://evmaths.jimdo.com/year­11/functions/?logout=1

2. Sketch the graphs of and
y=x2
y=x2
­2
y=x2
+3
vertex:
line of symmetry:
vertex:
line of symmetry:

3. Conclusions:
parabola moves upwards
parabola moves downwards
vertex:
line of symmetry:
( 0 , k )
x = 0
Translation k units along
y­axis
k > 0
k < 0

4. Try these two graphs in your calculator
y =2 x2
­ 2x ­ 4 y = ­ x2
+ 4x ­ 3
What is the y­intercept in each case?

5. In y = a x2
+b x +c
the coefficient c represents the y­intercept
of the parabola
State clearly the y­intercept of these parabolas:
y = x 2
+ 1
y = ­9 + 5x +x 2
y = x 2
­ x­ 2

6. Use your calculator to plot the graphs of:
y = 3 x2
­ 2 y = 5x 2
­ 2
y = ­3 x 2
­ 2
What is the effect of the coefficient a ?
y = ­5x 2
­ 2

7. Conclusions:
f(x) = a x 2
+ bx + cThe graph of when
a > 0
a < 0
• the parabola is positive, goes upwards
• the parabola has a minimum point
• the parabola is negative, goes downwards
• the parabola has a maximum point.

8. Match each formula with its graph

9. The graph shown has equation y = ax2
­ 2x + c.
Find the values of a and of c.

10. The graph has equation
Find the values of a and c.

11. Write the following quadratic functions in
the general form y=a x2
+ bx +c
State the y­intercept of each function

12. x
y

13. Find the roots of the following functions:

14. For each of the following quadratic functions
y = 2(x­3)(x+1) y = ­3(x­1)2
+ 4
(a) Write down the y ­intercept of their graphs
(b) Use your GDC to find
(i) the coordinates of the vertex on their
graphs.
(ii) the equation of the line of symmetry
(ii) the roots
(c) Write down the value of a and of b.

15. Solve Ex 1 A page 5

16. Attachments
Parabola canonica.ggb
Cambios cuadratica.ggb
QUADRATIC FUNCTIONS I 2010.doc
Transformaciones Función Cuadrática.ggb
Vertical translation of parabola.ggb
Vertical stretch of parabola.ggb
Horizontal translation of parabola.ggb
Translations in parabola.ggb