add math(f4) quadratic function 3.1

CHAPTER 3

QUADRATIC FUNCTION

3.1 QUADRATIC FUNCTION AND GRAPH

3.1.1 Recognising a Quadratic Function

3.1.2 Plotting graph of Quadratic Functionsa)Based on given tabulated valuesb)Based on a given function

3.1.1 Recognising a Quadratic Function

where a, b and c are constants and a ≠ 0. Note that the highest power of

variable x is 2.

cbx2axf(x) ++=

Example:

xxxf 6)( 2 −=1588)( 2 ++= xxxf

235)( 2 +−−= xxxf

)2)(1()( −+= xxxf

Example 1: Determine whether the given functions is Quadratic Function. If so, take the values of a, b and c.

a)

b)

c)

d)

23)( 2 +−= xxxf

2325)( xxxf −−=

)2()( −= xxxf

)3(2)( 2xxxf −=

Solution:

a)the highest power of x is 2,

thus f(x) is a quadratic function with a=1, b= -3 and c= 2

23xxf(x) 2 +−=

Solution:

b)

the highest power of x is 2, thus f(x) is a quadratic function with a=-3, b= -2 and c= 5

52x3x

3x2x5f(x)2

2

=−−=−−=

Solution:c)

the highest power of x is 2, thus f(x) is a quadratic function with a=1, b= -2 and c= 0

2xx

2)x(xf(x)2 −=

−=

Solution:d)

the highest power of x is 3, thus f(x) is not a quadratic function

3

2

2x6x

)x2x(3f(x)

−=−=

Explore by using Geometer’s Sketchpad

software.

WORKSHEET 13 MINUTES

2. Express each of the following quadratic function in the form of . Hence, state the values of a, b and c.

1.State which of the following are quadratic function

cbxaxxf ++= 2)(

23)() xxxfa −−= 21

)()2

+=x

xfb

xxxfb 42

1)() 2 −=

2324)() xxxfa −−=

86)() 2 +−= xxxfc

Solution

3.1.2 Plotting graph of Quadratic Function

a) Based on given tabulated valuesb) By tabulating values based on a given

function.

Based on given tabulated values

• Example 2The table below shows the tabulated values of Quadratic Function of f(x). By using suitable scale, plot the graph of function of f(x)

7-2-1-2-127f(x)

3210-1-2-3x

The table below shows the tabulated values of Quadratic Function of f(x). By using suitable scale, plot the graph of function of f(x)

1341413f(x)

210-1-2x

Quiz (3 minutes)

Based on a given function

• Example 3Given function of f(x)=1-3x2 .Tabulate values for x and f(x) -2≤ x ≤ 2. Then, by using suitable scale, plot the graph of f(x)=1-3x2

Solution

• GSP

Conclusion

Students were able to:• recognizes quadratic functions • plot quadratic functions graphs

– based on given tabulated values– by tabulating values based on given functions

THANK YOU.ALL THE BEST