UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...
Quadratic Functions.pptx
1. Quadratic Functions
Learning Targets
• Give an example of real life situations
using quadratic functions.
• Differentiate quadratic functions from
linear functions.
2. Match the items in column A with the item in column B that
is related to it.
Column A Column B
A newborn baby children
A bar code in a shop date of birth
A real number square of that number
A mother price
3. A newborn baby is related to his or her date of birth. This
relationship is a function since to each baby have its own date of
birth. In other words, no baby can have two dates of birth.
-3
-2
1
0
3
9
4
1
0
9
x x2
A bar code in a store is related to a price. This also shows a
function since to each bar code, there corresponds a price. In
fact, no bar code can have two or more different prices.
A real number is related to a square of that number. This is
also a function since to each real number there corresponds a
square of the number. In other words, no real number can have
two or more different squares.
On the other hand, a mother can have two or more
children. Hence, this relation is NOT a function.
4. DOMAIN RANGE
Correspondence
FUNCTION
A function is a correspondence between a first set called domain, and
a second set, called range, such that each member of that domain
corresponds to exactly one member of the range.
QUADRATIC FUNCTION
A quadratic function is polynomial of degree 2 and defined by the
equation 𝒇 𝒙 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄, where a, b and c are real numbers and a≠ 0.
6. Quadratic Term Linear Term Constant Term
TAKE NOTE!
The most general form of quadratic function is 𝒇 𝒙 = 𝒂𝒙𝟐
+ 𝒃𝒙 + 𝒄 or 𝒚 =
𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄.
The first term in the quadratic function 𝒂𝒙𝟐 is called quadratic term, 𝒃𝒙 is the
linear term and 𝒄 is the constant term.
𝒇 𝒙 = −𝟑𝒙𝟐 + 𝟑𝒙 + 𝟏
6x2
𝒇 𝒙 = 𝟔𝒙𝟐 − 𝟐𝒙 + 𝟕
𝒇 𝒙 = (𝟓𝒙 + 𝟑)𝟐−(𝟐𝒙 + 𝟓)𝟐
-3x2
21x2
-2x
3x
10x
7
1
-16
7. 𝒇 𝒙 = (5𝑥 + 3)𝟐
−(2𝑥 + 5)2
𝒇 𝒙 = (25𝑥𝟐+𝟑𝟎𝒙 + 𝟗) − (4𝑥2+𝟐𝟎𝒙 + 𝟐𝟓)
𝒇 𝒙 = 25𝑥𝟐
+ 𝟑𝟎𝒙 + 𝟗 − 4𝑥2
− 𝟐𝟎𝒙 − 𝟐𝟓
𝒇 𝒙 = 21𝑥𝟐 + 𝟏𝟎𝒙 − 𝟏𝟔
SECOND DIFFERENCE TEST
A relation f is a quadratic function if equal differences
in the independent variable x produce nonzero equal
second difference in the function value f(x).
13. Learning Targets
transform the quadratic function
defined by 𝑦=ax²+bx+c into the form
y=a(x-h)2 + k.
Determine the values of (h,k0) using
completing square or the formula:
𝒉 =
−𝒃
𝟐𝒂
and 𝒌 =
𝟒𝒂𝒄−𝒃𝟐
𝟒𝒂
14. QUADRATIC FUNCTION IN THE FORM
y=ax2+bx+c into y = a(x-h)2 + k or VICE VERSA
Using the principle of completing the square, we can rewrite the quadratic
function is 𝒇 𝒙 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 into is 𝒇 𝒙 = 𝒂(𝒙 − 𝒉)𝟐 + 𝒌 where (h, k) is the vertex.
𝒇 𝒙 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 Standard form of the quadratic function
𝒇 𝒙 = 𝒂(𝒙𝟐 +
𝒃
𝒂
𝒙) + 𝒄 Factor a form first 2 terms
𝒇 𝒙 = 𝒂 𝒙𝟐
+
𝒃
𝒂
𝒙 +
𝒃𝟐
𝟒𝒂𝟐 + 𝒄 −
𝒃𝟐
𝟒𝒂𝟐
𝒇 𝒙 = 𝒂(𝒙 +
𝒃
𝟐𝒂
)𝟐 +
𝟒𝒂−𝒃𝟐
𝟒𝒂
Letting 𝒉 =
−𝒃
𝟐𝒂
and 𝒌 =
𝟒𝒂𝒄−𝒃𝟐
𝟒𝒂
f(x) = a(x-h)2 + k
20. GRAPHS OF QUADRATIC FUNCTION
All quadratic functions have graphs
similar to this graph. This U-shaped is
called a parabola. 𝑷𝒂𝒓𝒂𝒃𝒐𝒍𝒂
𝒗𝒆𝒓𝒕𝒆𝒙
( 0, -1 )
The “turning points” of the graph is
called the vertex of the parabola.
The parabola is symmetric with respect
to a line that passes through the vertex.
This line is called the axis of symmetry. It
divides the parabola into two parts so
that one part is a reflection of the other
part.
𝒂𝒙𝒊𝒔 𝒐𝒇 𝒔𝒚𝒎𝒎𝒆𝒕𝒓𝒚
21. Vlog it!
1. Choose 3 things/objects in your house that will represent
graph of quadratic function.
2. Show it and explain how it will represent a graph of quadratic
function or concept quadratic function by making a short
vlog.
3. You will be graded using the criteria below:
Presentation 5
Content 6
Explanation 9
20
