add math(f4) quadratic function 3.1
TRANSCRIPT
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CHAPTER 3
QUADRATIC FUNCTION
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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
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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) ++=
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Example:
xxxf 6)( 2 −=1588)( 2 ++= xxxf
235)( 2 +−−= xxxf
)2)(1()( −+= xxxf
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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 −=
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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 +−=
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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
=−−=−−=
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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 −=
−=
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Solution:d)
the highest power of x is 3, thus f(x) is not a quadratic function
3
2
2x6x
)x2x(3f(x)
−=−=
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Explore by using Geometer’s Sketchpad
software.
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WORKSHEET 13 MINUTES
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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
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Solution
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3.1.2 Plotting graph of Quadratic Function
a) Based on given tabulated valuesb) By tabulating values based on a given
function.
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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
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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)
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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
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Solution
• GSP
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Conclusion
Students were able to:• recognizes quadratic functions • plot quadratic functions graphs
– based on given tabulated values– by tabulating values based on given functions
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THANK YOU.ALL THE BEST