a. Pada pembelajaran ekspositori tidak menekankan penonjolan aktivitas fisik seperti aktivitas mental siswa.
b. Kegiatan terpusat pada guru sebagai pemberi informasi bahan pelajaran. c. Pengetahuan yang didapat cepat hilang.
2.1.7 Tinjauan Materi Fungsi Kuadrat
Materi pokok yang dipilih oleh peneliti adalah materi fungsi kuadrat, dengan penjabaran dalam bahasa Inggris sebagai berikut:
2.1.7.1 The Understanding of Quadratic Function
The general form of quadratic function is:
Where a, b, and c are real numbers and In the form of the
quadratic function above, the value of may be changeable along the real
number line, whereas the value of depends on the value of . Hence, is
called independent variable and is called dependent variable.
The quadratic function is often written in the form of curve equation where are real numbers and . For example
known function The value of function for
and is a follows.
, and
The graph of a quadratic function has a special graph form, that is parabolic. Parabola with an equation
has two possibilities, they are opened upward or downward observe figure 2.3.
If the parabola is opened upward, it has minimum extreme. Whereas the parabola is opened downward, it has maximum extreme.
2.1.7.2 Depicting Quadratic Function Graph
The simple way to depict a quadratic function ggraph of
is by choosing several real numbers from domain and find the value of function
for each value of . Chosen so obtained actually 3 points is enough, but for beginner it is better of 5 points. The points are depicted in the Cartesian plane then
connected so that they form a parabola smooth curve.
Example 1: Depict a diagram of parabola graph of
Solution: To find out 5 points that obey
we make the following value table.
-2 -1
1 2
4 1
1 4
-2,4 -1,1
0,0 1,1
2,4
Figure 2.3
Table 2.2 Tabel of graph of
Five points
which obey
are and . The points are
placed at Cartesian plane then connected so that they form a smooth curve as visible at the following figure is shaped.
We have understood that a parabola is symmetrical. It means that a parabola has a symmetrical axis. From the picture of example 1 we can see that
the symmetrical axis of graph of is
-axis or line of The intersection between a symmetrical axis and the curve is called a vertex. From the
picture we can see that the vertex of parabola of is 0, 0.
Example 2 :
Without depicting a graph, determine whether the following graph is opened upward or downward.
a. b.
Solution : a.
, , means the graph is opened up ward.
b. ,
means the graph is opened down ward.
If the formula of quadratic function has been in the form of perfect square, so without drawing a graph we are able to determine the equation of symmetrical
axis and coordinate of its vertex.
1 The symmetrical axis,
2 The vertex =
2 3
-2 -1 Figure 2.4
At the previous description, if we draw a diagram of quadratic function graph parabola, we determine 5 points which fulfill, then connect the points to
form a parabola. Actually the most important matters to be determined in drawing the graph function of
are : 1.
a vertex 2.
x-intercept The condition to intersect
axis is Substitute
into acquired
. i.
: intersects -axis at two points. ii.
: touches -axis. iii.
: not intersect -axis. 3.
y-intercept The condition to intersect
-axis is Substitute
into . So the y-
intercept is Coordinate of parabola vertex
is
We come by conclution about the position of parabola toward axis
observed from a and D value at the curve equation is:
The vertex of quadratic function graph is commonly called extreme point. Ordinat of extreme point, namely
is called extreme value. whereas abscissa of extreme point, namely
is called extreme factor- making-extreme point.
2.1.7.3 Positive and Negative Definites
