INTRODUCTION TO QUADRATIC EQUATIONS | GRADE 9
Summary
TLDRThis educational video script targets grade 9 students delving into quadratic equations. It introduces quadratic equations as those with the highest variable exponent of 2. The script defines the equation's degree, explains the standard form ax^2 + bx + c = 0, and distinguishes between complete and incomplete quadratic equations. It guides students through identifying quadratic terms, linear terms, and constants in equations. The video also includes exercises to test understanding and concludes with a summary of key concepts, promising further exploration in upcoming videos.
Takeaways
- 📘 The first topic in grade 9 math is quadratic equations.
- 🔢 A quadratic equation is defined as an equation with the highest exponent of the variable being 2.
- 📚 The objectives of the video include understanding what a quadratic equation is, recognizing examples, and solving exercises with accuracy.
- 📐 The degree of an equation is determined by the highest exponent of the variable, which for a quadratic equation is 2.
- 🔍 Examples are provided to differentiate between quadratic and non-quadratic equations based on the highest exponent.
- 📝 The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are real numbers and 'a' cannot be zero.
- 🔑 The terms in a quadratic equation are identified as the quadratic term (ax^2), the linear term (bx), and the constant term (c).
- 🧩 Incomplete quadratic equations can lack one or more of the terms (bx or c), but 'a' must not be zero.
- 📉 The video provides exercises to test the understanding of identifying quadratic equations.
- ✅ The video concludes with a summary emphasizing the definition, standard form, and components of a quadratic equation.
Q & A
What is the definition of a quadratic equation?
-A quadratic equation is an equation where the highest exponent of the variable is 2.
What is the significance of the term 'quadratic' in quadratic equations?
-The term 'quadratic' comes from the word 'square' because the variable gets squared, like x squared.
What is the standard form of a quadratic equation?
-The standard form of a quadratic equation is written as ax squared plus BX plus C equals 0, where a, B, and C are real numbers and a must not be equal to 0.
What are the three terms in a quadratic equation?
-The three terms in a quadratic equation are the quadratic term (ax squared), the linear term (BX), and the constant term (C).
Why must 'a' not equal zero in a quadratic equation?
-In a quadratic equation, 'a' must not equal zero because if 'a' is zero, the equation is no longer quadratic.
Can you provide an example of a quadratic equation?
-An example of a quadratic equation is 3x squared minus X minus 5 equals 0.
How do you identify if an equation is quadratic by looking at its highest exponent?
-An equation is identified as quadratic if the highest exponent of the variable is 2.
What is an incomplete quadratic equation?
-An incomplete quadratic equation is a quadratic equation that may lack one of the terms (BX or C), such as ax squared plus BX equals 0 or ax squared equals 0.
What happens to the degree of an equation if the highest exponent is not 2?
-If the highest exponent is not 2, the degree of the equation is determined by that highest exponent, making it not a quadratic equation.
How do you find the values of 'a', 'B', and 'C' in a quadratic equation?
-In a quadratic equation, 'a' is the coefficient of the x squared term, 'B' is the coefficient of the x term (or 0 if there is no x term), and 'C' is the constant term.
What is the significance of the equal sign in a quadratic equation?
-The equal sign in a quadratic equation signifies that the expression on the left is equal to the expression on the right, making it an equation.
Outlines
📚 Introduction to Quadratic Equations
This paragraph introduces the topic of quadratic equations for grade 9 mathematics students. It emphasizes the importance of understanding the concept of quadratic equations, which are equations with the highest exponent of the variable being 2. The video aims to teach students to recognize and provide examples of quadratic equations. The learning objectives include knowledge, skills, and attitude towards solving quadratic equations with honesty and accuracy. The explanation begins with the definition of a quadratic equation, its degree, and the significance of the exponent in determining the degree of an equation.
🔍 Identifying Quadratic Equations
The paragraph continues with examples to help students identify which equations are quadratic. It explains that the highest exponent of the variable must be 2 for an equation to be considered quadratic. The script walks through several equations, discussing why some are quadratic and others are not, based on the highest exponent present. It also clarifies that even if an equation appears not to have an exponent of 2, it may still be quadratic if simplified correctly.
📘 Expanding and Simplifying Quadratic Equations
This section delves into more examples of quadratic equations, showing how to simplify expressions to reveal the quadratic form. It demonstrates the use of the distributive property to expand expressions and how multiplying binomials results in a quadratic equation. The paragraph explains the standard form of a quadratic equation, ax^2 + bx + c = 0, and defines the terms: quadratic term (ax^2), linear term (bx), and constant term (c). It also stresses that 'a' must not be zero for the equation to remain quadratic.
📖 Incomplete Quadratic Equations
The paragraph discusses incomplete quadratic equations, which may lack one of the terms (bx or c) in the standard form. It provides examples and explains how to identify the values of a, b, and c in various scenarios. The importance of 'a' not being zero is reiterated, even if b or c can be zero. The section ensures students understand that a quadratic equation must have the highest variable exponent of 2.
📝 Practice and Summary
The final paragraph involves practice questions for students to apply their knowledge of identifying quadratic equations. It includes multiple-choice questions to test comprehension of the concept. The paragraph concludes with a summary of the key points learned: the definition of a quadratic equation, the standard form ax^2 + bx + c = 0, and the importance of the coefficient 'a' not being zero. The instructor also hints at further discussions on quadratic equations in upcoming videos.
Mindmap
Keywords
💡Quadratic Equation
💡Exponent
💡Degree of an Equation
💡Standard Form
💡Quadratic Term
💡Linear Term
💡Constant Term
💡Incomplete Quadratic Equations
💡Distributive Property
💡FOIL Method
💡Exercises
Highlights
Introduction to quadratic equations in grade 9 math.
Objectives of the video include understanding, illustrating, and accurately solving quadratic equations.
Definition of a quadratic equation: an equation with the highest variable exponent of 2.
Explanation of the term 'quadratic' and its relation to the variable being squared.
Identification of the degree of an equation based on the highest variable exponent.
Examples of quadratic equations and distinguishing them from non-quadratic equations.
Simplification of expressions to reveal the highest exponent and identify quadratic equations.
Use of the distributive property to simplify expressions and identify quadratic equations.
Explanation of the standard form of a quadratic equation: ax^2 + bx + c = 0.
Emphasis on the condition that 'a' must not be equal to zero in a quadratic equation.
Identification of the quadratic term, linear term, and constant term in a quadratic equation.
Examples of incomplete quadratic equations and how to identify their components.
Exercises to test the understanding of identifying quadratic equations.
Multiple-choice questions to reinforce the concept of quadratic equations.
Summary of the key points about quadratic equations learned in the video.
Anticipation for more detailed discussion on quadratic equations in upcoming videos.
Transcripts
[Music]
hello everyone especially to our
students who really love to learn
mathematics this video will discuss the
first topic in grade 9 math and it's all
about quadratic equation so please
listen carefully or if you want you can
also get your notebook and pen and take
down some important notes about our
topic
our objectives in this video will be the
first M DLC or the most essential
learning competency in mathematics 9 and
that is to illustrate quadratic equation
we will be able to know what is a
quadratic equation and for the KS a
objectives we have this for the
knowledge you will be able to recognize
and give examples of a quadratic
equation for the skills illustrate
quadratic equation and for the attitude
or values you will be answering a given
exercises with honesty and accuracy now
let's start what is a quadratic equation
what does it mean and what is it all
about the named quadratic comes from
what meaning square because the variable
gets squared like x squared therefore a
quadratic equation is an equation where
the highest exponent of the variable
usually X is 2 so as you can see from
the definition it is an equation meaning
to say it must have an equal sign and
remember that the highest exponent of
the variable is to just our recap our
recall about the exponent the exponent
is written on the upper right of a
certain number or a variable just like
this 1 X raise to 4 4 is our exponent so
here in a quadratic equation the highest
exponent is 2 that is why it is called
as equation of degree 2
the degree of an equation is determined
through the highest exponent of the
variable in an equation so called an
highest exponent now if some equation is
to the degree of equation is to if the
highest exponent is 3 the degree of
equation is 3 so it has to turn mean by
the highest exponent of the variable let
us now have the examples of a quadratic
equation
we have now five equations here and
we're going to identify which among
these equations are quadratic and which
among are not quadratic equation let's
begin with the first equation and that
is 3x squared minus X minus 5 is equal
to 0 what do you think is the highest
exponent here the highest exponent of
this equation is 2 therefore this is a
quadratic equation next how about this
one
5x minus of 3 is equal to 0 it says a
quadratic or not quadratic equation what
is the highest exponent of this equation
yes the highest exponent is not two but
one so therefore this is not a quadratic
equation next how about the third
equation here we have x cubed plus 4x
minus 3 x squared is equal to zero do
you think it is also a quadratic
equation no it is not a quadratic
equation because what is the highest
exponent here the highest exponent here
is 3 right not to although we can see
two here as our exponent 2 is not the
highest exponent but the highest
exponent is 3 therefore this is also not
a quadratic equation next is the year
four equation here 2x squared plus 12x
is equal to 0 what do you think is the
highest exponent of this equation yes
the highest exponent is 2 therefore this
is a quadratic equation and the last one
x squared minus 4x is equal to 0
you can see here that the highest
exponent is 2 and it is a quadratic
equation ok so you can notice here that
all the quadratic equation has the
highest exponent of 2 unlike on the nut
quadratic here the axe exponent here is
1 and the highest exponent here is 3 so
we can now easily say that a quadratic
equation must be the highest exponent of
a quadratic equation must be 2 but let
us have more examples
let us now have the examples of a
quadratic equation another example of a
quadratic equation is this x times the
quantity of X plus 2 is equal to
negative 1 but you will notice that
there is no 2 exponent here so how come
that this is an example of a quadratic
equation the reason is that we need to
simplify it first or find its product
and the product of this is a quadratic
equation let's see we will apply the
distributive property of multiplication
to get its product the first step here
is to multiply X to the first term
inside the parentheses and that is X at
some times X the answer will be x
squared we will just simply add the
exponent in multiplying this next step
we will multiply X and the second in to
the second term inside the quantity and
that is 2x times 2 the answer is 2x plus
2x and just copy negative 1 equals
negative 1 just like this x squared plus
2x is equal to negative 1 but a
quadratic equation must be equal to 0 so
we will transpose or move the negative 1
here to this side and as we move it we
will change the sign it will become
positive 1/4 plus 1 therefore the
product of this is x squared plus 2x
plus 1 is equal to 0 you can see now
that we have the highest exponent of 2
in its product therefore this is also an
example of a quadratic equation another
example we have X
quantity x squared X plus 2 times
quantity of X minus 5 is equal to 0 this
is a multiplication of two binomials and
this is also considered as a quadratic
equation because we all know that if we
multiply this the product is a quadratic
equation or it will become x squared and
in getting the product we will use the
foil method first term outer inner and
last turn okay let's see X plus 2 our
quantity X plus 2 times the quantity X
minus 5 is equal to 0 we will be
multiplying the first term ok x times X
the answer is x squared followed by the
all the outer term the outer term is
this X and negative 5 so x times
negative 5 we have negative 5 X followed
by the inner term and that is 2 and x2
times X the answer is positive 2x and
for the L the last term that is 2 and
negative 5 2 times negative 5 the answer
is and negative 10 and then copy equal
to 0 but we can simplify negative 5 and
negative 1 positive 2 right we can add
the product of oh and I so negative 5 X
plus 2 X since they are or they have sin
term we can simplify this so the answer
is 3 negative 3x therefore the final
product is x squared minus
3x minus 10 is equal to 0 you see here
that the highest exponent of the product
is 2 therefore that this example is also
a quadratic equation the standard form
of a quadratic is written as ax squared
plus BX plus C is equal to 0 where a B
and C are real numbers and always
remember that a must not be equal to 0
because if a is equal to 0 this is not
if I'd Radek equation anymore
okay let us find out more about it
the first term that we have in our
periodic equation ax squared is pulled
as our quadratic term okay so you marrow
x squared Union quadratic term Athena
power at the end while the BX or you
excellent or one exponent that is Lin
your turn and the last one young Salam
or your number lamb that is what we call
the constant term we have now three x
squared minus X plus five equals to 0
what will be our quadratic leaner and
constant term the quadratic term has the
x squared or the two exponent here we
have the x squared that is the quadratic
term the linear term okay that is the
negative x or it has a one exponent
right variable having a one exponent
this
our leader term and the last term the
number only that is what we call the
constant term this time we are going to
find the values of a B and C of a
quadratic equation we have the equation
3x squared minus X plus 5 is equal to 0
what will be the a B and C here a is
equal to 3 it can be seen beside the x
squared or the variable having this 2
exponent the number beside it is the
value of a how about the value of B the
value of B is found here the number
beside the X but you cannot see a number
here right but we can still remember
that it has an invisible one here and no
need for us to write it down in this
equation but if we are asked to find B B
is equal to negative 1 again it has an
invisible 1 here and if we want to find
the value of C the value of C here is
negative 5 I'm sorry positive 5 C is
positive 5 or the letter C the value of
C can be seen on the constant term how
about this one x squared plus 4x minus
21 is equal to 0
what is a and what is B and what is here
a is there is no number written here but
it has an invisible one right so X is a
is equal to 1
how about linear term or the B the BS
for B is equal to 4 and C the C here the
constant term is negative 21
maybe I'll include the negative here
again do not include the variable in
finding the values of a B and C we
understand now that the standard form of
a quadratic equation is ax squared plus
BX plus C is equal to 0 but there are
cases that we also have what we called
incomplete quadratic equations
what are those incomplete quadratic
equations example is this one ax squared
plus BX is equal to 0 as you notice
there is no C right example of this
equation 2x squared plus 8x is equal to
0 if we are asked to find the a B and C
this will be the answer is equal to 2 B
is equal to 8 and C is equal to 0 C is
equal to 0 because there is no C here
right
there's no see another incomplete
quadratic equation is in the form of AX
squared plus C is equal to 0 example x
squared minus 9 is equal to 0 if we are
asked to find the values of a B and C a
is equal to 1 B is equal to 0 because
there is no B or there's no linear term
here but we only have C C is equal to
negative 9 another case is that a x
squared
still this is and
the quadratic equation but is it is
incomplete and there is no B and C
example 2x squared is equal to zero if
we are asked to find the a B and C a is
equal to 2 B is equal to 0 and C is
equal to 0 both B and C are equal to 0
remember that in a quadratic equation B
and C can be equal to 0
yes it can be but it must not be a is is
not equal to 0
hey in a selector a dhaba indicia equal
to 0 because if we let a is equal to 0
then our equation is not a quadratic
anymore right
okay so let's have some exercise which
of the following equations are quadratic
equations number one 3x minus 2 is equal
to 0 what do you think is it put that
peak or not
hey the answer is not quadratic okay we
don't have to exponent right number 2 X
plus the 3x squared is equal to 0
I said quadratic or not the answer is
yes it is a quadratic we have here our 2
as the highest exponent next number 3 2
times the quantity of X minus 4 is equal
to 0 is it quadratic or not the answer
is not good body even though we multiply
this 2 times X the answer is 2x
ok the product of this is not equal
ratification
and the last one how about the last one
x times the quantity of X plus 3 minus 5
is equal to 0 is it quadratic or not the
answer if we get the product of this we
have a quadratic equation okay very good
so did you get it all correctly I hope
so
next question is a multiple-choice write
the letter in words of the correct
answer
number 5 question which of these
equations in a straight quadratic
equation is it a quantity X plus 3 plus
8 is equal to 0 B opps pair of x plus 3
is equal to 0 C X plus y is equal to 0
or a T X cube is equal to 2x what is the
answer the correct answer is B Square of
X plus 3 is equal to 0
next question number 6 it is a
polynomial equation of degree 2 I said a
quadratic equation B linear equation C
quadratic inequality the linear
inequality what will be the answer the
answer here is yes quadratic equation
number 7 question which of the following
is the standard form of a quadratic
equation is it a ax plus B greater than
or equal to 0 B ax plus B is equal to 0
C ax squared plus BX plus C is greater
than or equal to 0 or D ax squared plus
BX plus C is equal to 0 what will be the
answer the correct answer is yes you're
correct D ax squared plus BX plus C is
equal to 0
eight which of the following real number
in the quadratic equation from ax
squared plus BX plus C equals zero
cannot be zero
is it a b c or none of this ileenium top
at the Indies zero socratic okay the
answer is a number nine which of the
following is the quadratic term of our
equation x squared minus 10x plus 25 is
equal to zero what is the quadratic term
is if a is 0 B negative 10x see x
squared be 25 so the answer is okay the
answer is C and we also have the last
one what is the value of B in this
equation 3x squared minus 12x is equal
to zero
it said 83 be negative 12 see three x
squared or be negative 12 X again if we
are asked to find B the answer is only a
number so the answer here is okay the
answer is negative 12 B negative 12 and
that's it so how was your score did you
pass at the test did you get at least
eight and about out of ten I hope so
now let's summarize what we have learned
today we understand now that the
quadratic equation is an equation where
the highest exponent of the variable is
2 and we have the standard form of
quadratic equation we have ax squared
plus BX plus C is equal to 0 and
remember a must not be equal to 0 and a
quadratic equation has a quadratic term
that is ax squared a linear term the X
and the constant term is our C okay we
will talk about more about quadratic
equation in my next video so please
stand by and watch me again on my next
video that's it bye bye
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