ILLUSTRATING QUADRATIC EQUATIONS || GRADE 9 MATHEMATICS Q1
Summary
TLDRThis educational video script introduces the concept of quadratic equations, focusing on how to identify and arrange them into standard form, ax^2 + bx + c = 0. It explains the significance of coefficients a, b, and c, and provides examples to illustrate the process. The script emphasizes the importance of a being non-zero and the equation retaining its quadratic nature even if b or c equals zero. It concludes with an encouragement to like, subscribe, and stay tuned for more informative content.
Takeaways
- π The video is about teaching how to identify the coefficients a, b, and c in a quadratic equation.
- π It emphasizes that a quadratic equation is in the standard form ax^2 + bx + c = 0, where a, b, and c are real numbers and a β 0.
- π The terms of the quadratic equation are defined: ax^2 is the quadratic term, bx is the linear term, and c is the constant term.
- π The video provides examples of how to rearrange equations into the standard form and identify a, b, and c values.
- π’ It explains that if 'a' is 0, the equation becomes linear, not quadratic.
- π« The importance of 'a' being a positive real number is highlighted to maintain the equation as quadratic.
- π Examples given include equations like x^2 - 5x + 3 = 0, where a=1, b=-5, and c=3.
- π The process of converting equations into standard form by moving terms and changing signs to fit ax^2 + bx + c = 0 is demonstrated.
- π The video clarifies that even if b or c equals 0, the equation can still be quadratic as long as a β 0.
- π It also covers how to handle equations with no linear term (b value) or no constant term (c value).
- π The video concludes by encouraging viewers to like, subscribe, and hit the bell for more content.
Q & A
What is a quadratic equation?
-A quadratic equation is a polynomial equation of the second degree, typically written in the form ax^2 + bx + c = 0, where a, b, and c are constants, and a β 0.
What are the three terms in a quadratic equation?
-The three terms in a quadratic equation are the quadratic term (ax^2), the linear term (bx), and the constant term (c).
What is the standard form of a quadratic equation?
-The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to zero.
How do you identify the values of a, b, and c in a given quadratic equation?
-To identify the values of a, b, and c, first write the equation in standard form. The coefficient of x^2 is a, the coefficient of x is b, and the constant term is c.
What happens if the coefficient 'a' in a quadratic equation is zero?
-If the coefficient 'a' is zero, the equation is no longer quadratic but becomes a linear equation.
What is the significance of the coefficient 'a' being positive in the standard form of a quadratic equation?
-The coefficient 'a' being positive in the standard form ensures that the quadratic term is correctly represented and that the equation is in its proper form.
How do you rewrite the equation x^2 - 5x + 3 = 0 in standard form?
-The equation x^2 - 5x + 3 = 0 is already in standard form, with a = 1, b = -5, and c = 3.
What is the quadratic term in the equation 7x^2 - 1/3x = 0?
-The quadratic term in the equation 7x^2 - 1/3x = 0 is 7x^2.
What is the linear term in the equation 6x^2 = 9?
-In the equation 6x^2 = 9, there is no linear term (no x term), so the linear term is considered to be 0.
How do you determine the constant term in the equation -8x^2 + x = 6?
-To determine the constant term in the equation -8x^2 + x = 6, you need to rearrange it to the standard form -8x^2 + x - 6 = 0, where the constant term is -6.
What is the process of converting a quadratic equation into standard form?
-To convert a quadratic equation into standard form, you need to rearrange the terms so that the equation is in the form ax^2 + bx + c = 0, ensuring that a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.
Outlines
π Introduction to Quadratic Equations
This paragraph introduces the concept of quadratic equations, explaining that they are mathematical expressions involving a variable raised to the second power. The standard form of a quadratic equation is ax squared plus BX plus C equals zero, where a, b, and c are real numbers and a is not equal to zero. The speaker emphasizes the importance of identifying the values of a, b, and c in any given quadratic equation. An example is provided where the equation x squared minus 5x plus 3 equals 0 is dissected to show that a equals 1, b equals negative 5, and c equals 3.
π Identifying Coefficients in Quadratic Equations
The speaker continues by discussing how to identify the coefficients a, b, and c in various quadratic equations. Examples are given to illustrate the process, such as transforming 9R squared minus 25 into a standard form where a equals 9, b equals 0, and c equals negative 25. Other examples include equations like 7x squared equals 1/3 X, which is rearranged to show a equals 7, b equals negative 1/3, and c equals 0. The importance of rearranging equations into standard form to clearly identify these coefficients is highlighted.
π Writing Quadratic Equations in Standard Form
This paragraph focuses on the process of writing quadratic equations in their standard form, ax squared plus BX plus C equals zero. The speaker provides several examples, such as x squared plus x equals four, which is rearranged to show a equals 1, b equals 1, and c equals negative 4. Other examples demonstrate how to handle equations without a linear term or with a constant term only. The emphasis is on correctly identifying the quadratic, linear, and constant terms and ensuring the equation is in the correct form.
π’ Understanding the Role of Coefficients in Quadratic Equations
The final paragraph delves into the roles of the coefficients a, b, and c in quadratic equations. The speaker clarifies that even if a or c equals zero, the equation remains quadratic as long as the variable is raised to the second power. Examples are used to illustrate how the equation changes when certain coefficients are zero, such as 3x squared minus X plus 5 equals 0, which shows a equals 3, b equals negative 1, and c equals 5. The speaker concludes by reminding viewers of the importance of the second-degree exponent in defining a quadratic equation.
Mindmap
Keywords
π‘Quadratic Equation
π‘Standard Form
π‘Coefficient
π‘Quadratic Term
π‘Linear Term
π‘Constant Term
π‘Example
π‘Graph
π‘Variable
π‘Degree
π‘Solving
Highlights
Introduction to quadratic equations and their standard form.
Explanation of how to identify the coefficients a, b, and c in a quadratic equation.
Clarification that a quadratic equation must have a second-degree term.
Example of identifying a, b, and c in the equation x squared minus 5x plus 3 equals 0.
Demonstration of rearranging equations into standard form with examples.
Explanation of how to handle equations without a linear term, such as 9R squared minus 25.
Illustration of converting equations like x squared plus x equals four into standard form.
Example of rearranging 7x squared equals 1/3X into standard form.
Discussion on the importance of a being a positive real number in the standard form.
Example of converting negative eight x squared plus X equals six into standard form.
Explanation of how to handle equations with multiple terms, such as 2x plus (x minus 1) equals 6.
Clarification on the necessity of a quadratic equation to have a second-degree exponent.
Example of identifying a, b, and c in the equation 3x squared minus X plus 5 equals 0.
Discussion on the implications of a, b, or c being zero in a quadratic equation.
Final summary and encouragement to like, subscribe, and watch more videos.
Transcripts
[Music]
Hyman Akiyama in this video entitled hi
Nathan
Inaba and quadratic equation by an open
18 since auditing a quadratic equation
into standard form ax squared plus BX
plus C equals 0
also a identify metonym a B and C value
given an quadratic equation so HoloNet
Maputo my melody tone mathematical
equations so Ungava Natan let's try to
identify the linear equations
si sagina 10
all right so Marinol on Tom Lehman
nananana Tutera Aetna lipid Sibylla ante
natal nothing linear equation now I know
burrito manga nitiram mathematical
equations so a to animate or ante natal
igniting quadratic equation pandoba not
in Malayalam and quadratic equation a
quadratic equation in one variable is a
mathematical sentence of the grid two
packs in a beam adding degree to second
degree dogmatic eaten attend so packing
dean athenian ajita eve exhibition bagua
Zhang to R squared or exponent nough to
ibig sabihin that is only a linear
equation
now since marin tae-young 2 which is on
the second degree then we can now
consider this as quadratic equation now
always remember that a quadratic
equation can be written
wedyn attention is so let into standard
form a new knob on standard form we have
a x squared plus BX plus C equals zero
where a B and C are real numbers and a
should not be equal to zero but and an
attendee not in a dapat indicia mug
equals zero or else
McGee linear equation lemon Ito no in
standard form it should be a positive
real number that and an opinion all
right let's have the parts of quadratic
equation what is a x squared this is our
quadratic term so we have three terms in
quadratic equation now what is what do
we call this
confirm bx is the linear term while c is
our constant term so in quadratic
equation in standard form ax squared is
the quadratic term BX is the linear term
and C is your constant term equals zero
okay so let's have an example let's try
to identify a B and C given the
following quadratic equation so I have
here x squared minus 5x plus 3 is equal
to 0 now I knew naba an a value B value
and C value of the given quadratic
equation so a is equal to 1 since we all
know that variable is only a little the
numerical coefficient of the variable is
always 1 next me is equal to negative 5
so after you NASA get nap and then C is
equal to 3 so Yan Lang para and PACU
Hannam e B and C you have to arrange it
first into standard form
parama who cannot enum value non a B and
C next for M squared plus 4 M plus 1 is
equal to 0 e is equal to 4 B is equal to
4 C is equal to 1 next in this give it
give an example 9 R squared minus 25 we
do not have the B value so what will be
the B value papa velasca doing some
idiotic equation so our a will be 9 me
will become 0
and then C is equal to negative 25 next
a is equal to 1/2 B is equal to 3
[Music]
okay didn't a man so last example
nothing Puma Poppins in your wallet and
constant term so therefore our C will be
zero
next how are we going to write a
quadratic equation into standard form so
remember our standard form must be
written in a x squared plus BX plus C
equals zero okay given the example x
squared plus x equals four so a lilypad
not in C for for us to have the value of
C and equated to 0 so we will have now x
squared plus X
aleady but not in C for so that will
become negative 4 is equal to 0 so we
can now get the value of a B and C is
equal to 1 B is equal to 1 C is equal to
negative 4 another example I have here 7
x squared is equal to 1/3 X so again let
us write this quadratic equation into
standard form so we will have 7 x
squared minus 1/3 X is equal to 0 so
even if at not in C one-third X and then
equate to 0 one-third X will become
negative so we will have now the value
of a which is 7 B is equal to negative
1/3 and C is equal to 0 since we do not
have
the value of Conda constant term
next we have here 6x squared is equal to
9 so let us arrange it into standard
form leap at 99 so Maggie
6x squared minus 9 remember NAFA pugna
really pata your non constant change the
sign Col du motto motto motto wishes are
equal symbol so therefore we will have
now is equal to 6 me is equal to 0 since
we do not have the linear term and then
C is equal to negative 9
next I have here negative eight x
squared plus X is equal to six
so first leap at 96 that will become
negative eight x squared plus X minus 6
gasps Emma giggling negativeness is six
and then equate to zero
now remember a guy anissina bacopa nina
non-standard form your age should be a
positive real number so since um a
methine veto a negative where the motion
a multiplied by negative one or whether
in among a divide moshe by negative one
so I'm Manya real and meet or mug to
change long tire lahat non-science
so you negative eight more Maggie Ginn
positive 8x squared young positive x
Maggie minus X u minus six Maggie Dean
plus 6 and then equals to 0 so we will
now have the value of a which is 8 B is
equal to negative 1 and C is equal to 6
neck's so it oh haha
young example so let's have an twist so
I have here say X multiplied by the
quantity of X minus 2 is equal to 10 so
we will have 3 x squared minus 1 again
sorry x squared multiplying I can say 3
x times X so when we are multiplying the
variable we are adding its exponent so
since Marron time X and the bias at Sal
all McGuigan to nasha so squared so 3
times 1 that is 3 X and X that is x
squared
next sign dominating minus 6 X 3 times
negative 2 that is negative 6 and since
we only have X 1 X or you will just copy
X and then bring down equals 10 mix a
lilypad Manhattan c10 can see that is
our constant term for us to write the
given quadratic equation into a standard
form so we will now have 3x squared
minus 6x minus 10 remember it should be
negative is equal to 0 so we can now get
a is equal to 3 B is equal to negative 6
and C is equal to negative 10
next I have here the quantity of 2x plus
5 and X minus 1 so Marin time the LaJuan
by a binomial so panin at insa is a soul
so first multiply 2x and X so that will
become 2x squared
next multiply 2x and negative 1 or minus
1 that will become negative 2x and then
5 times X that is 5x and then 5 times
negative 1 that will become negative 5
equals 6 so we will now have 2x squared
plus 3x pocket casts a mere entire
negative 2 and positive 5 so McGee
positive 3x so Buffett positive 3
because 5 is bigger than at the absolute
value of 5 is bigger than the absolute
value of negative 2 and then bring down
negative 5
bring down negative 6 next so evenly but
not in C negative 6 so McGee 2x squared
plus 3x minus 5 plus 6 remember negative
share soap agni-v but not in McGee
positive 6 is equal to 0
now since Marant IM dalja want constant
term we will combine this two so McAfee
anti-human and 2x squared plus 3x plus 1
equals 0 so we will now have a is equal
to 2 B is equal to 3 and C is equal to 1
always remember that the standard form
must be a x squared plus BX plus C
equals 0
okay so boo ha nothing's a gotten it all
let's think about this
consider 3x squared minus X plus 5 is
equal to 0 what is a in the equation
so since nifer arranged nasha into
standard form Adelina natima fajita and
value non e and that is 3 if a is equal
to 0
well the equations still be quadratic no
a guy yeah - in a bhikkhu pnina
if a will become 0 then the value of it
will well i Maggie equals ax 0 so that
will become linear equation neck next
what is B in the equation so B is equal
to a negative 1 if B will if B is equal
to 0 well the equation still be
quadratic yes we can still have a and C
what is C in the equation that is 5 if C
is equal to 0 well the equation still be
quadratic yes always remember the
quadratic equation must have a second
degree exponent so hi Edna and be at
sinatun among equals a zero that is
still awkward thank you for watching
this video I hope you learned something
don't forget to Like subscribe and hit
the bell button so our Walmart channel
just keep on watching
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