# Student Activity 3a   2, 1, 0,1, 2,3, 4,5, 6 ```:
Student Activity 3a

Tables for each of the functions below are drawn on the next page of this document for x  2, 1,0,1, 2,3, 4,5,6 .
What do you notice about all the tables?
Using the same axes and scales plot the points for each function and join up the points to form an appropriate curve.
Polynomial in the form
f ( x)  ax  bx  c
f ( x) ( x  r )( x  s)
2
f ( x) ( x  h)  k
2
State the
shape of
the graph
and
whether it
opens
upwards or
downwards
x–
intercepts
(algebraic
method
and using
the graph)
y–
intercept
(algebraic
method
and using
the
graph)
Maximum/
minimum
point as an
ordered
pair and
labelled as
max or
min
Real
root(s)
of
f(x) =0
Equation
of the
axis of
symmetry
f
Solve
(2.7) f(x)
=8
For what x
values
is f(x)
positive?
f ( x)  0
For what x
values is
f(x)
negative?
f ( x)  0
y  x2  4 x  5
y  ( x  5)( x  1)
y  ( x  2)2  9
1. What do you notice about all of the graphs and all of the three functions you have plotted in this activity?
2. What items of information about the graph can you read from the equation y  x  4 x  5 before you plot its graph?
2
3. What extra items of information can you tell about the graph in this factored form y  ( x  5)( x  1) ?
4. What are the roots of y  ( x  5)( x  1)?
5. What are the roots of y  ( x  r )( x  s)
6. What extra item of information can you tell about the graph when f(x) is in the form y  ( x  2)  9 ?
2
7. How does knowing the x- intercepts (roots) help us to find the axis of symmetry?
Draft 01 © Project Maths Development Team 2011
3a
Page 1 of 4
For what
x values is
f(x)
increasing?
For what
x values is
f(x)
decreasing?
:
x
x
y  x2  4 x  5
( x, y)
x
y  ( x  5)( x  1)
( x, y)
x
y  ( x  2)2  9
( x, y)
Student Activity 3a
Plot the points and draw the graph for each of the functions in the tables on this page.
10
y
9
8
7
6
5
4
3
2
1
−3
−2.5
−2
−1.5
−1
−0.5
x
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
Draft 01 © Project Maths Development Team 2011
3a
Page 2 of 4
Student Activity 3a
Write the equation for each graph below in factored form i.e. y  ( x  r )( x  s) and also in the
general form y  ax 2  bx  c .
1.
3.
2.
4.
Draw x and y axis and draw the graph of a quadratic
function below giving its equation in the form
y  ( x  r )( x  s) .
5.
Draft 01 © Project Maths Development Team 2011
3a
Page 3 of 4
Student Activity 3a
Working in pairs, sketch the following graphs on the axes below.
Note particularly the intercepts on the axes and whether the graph has a local maximum or local
minimum. (Check the sign of y values for x values between the roots.)
Verify that you are correct by using a graphing calculator or graphing software such as GeoGebra if
y  ( x  2)( x  3)
y  ( x  2)( x  3)
y  ( x  4)2
y  x( x  3)
y  (2  x)( x  1)