Introduction to write quadratic function in vertex form
General form of a quadratic equation is y= ax2+ bx +c where a,b and c are real numbers and a 0.The graph of the quadratic equation is a parabola (either up or down). Let us assume that this parabola has its vertex at (h,k), then we can write the quadratic equation in vertex form as y= a(x-h)2+k.
There are 2 methods to write quadratic equation in vertex form.
Click on the link to learn about "quadratic equation formula"
1. Using completing the square method
2. Using vertex formula
VERTEX : For any two edges that meet at an end – point, there is a third edge, that also meets them at that end – point. This point of intersection of three edges of a cuboid is called a vertex of the cuboid.
The vertices of the cuboid in the figure are A, B, C, D, E, F, G, H.
Clearly, a cuboid has 8 vertices.
Thus, we see that the twelve edges of a cuboid can be grouped into three groups such that all edges in one group are equal in length. This means that twelve edges of a cuboid can have only three distinct lengths. Usually, the longest of these is called the length of the cuboid and out of the remaining two, one is called the breadth or width and the other height of the cuboid.
BASE AND LATERAL FACES : Any face of a cuboid may be called the base of the cuboid. In that case, the four faces which meet the base are called the lateral faces of the cuboid.
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Let us learn about "Antiderivative Calculator" and as you know in previous blog we learned about "Molarity Calculator" which was very interesting.
Antiderivative Calculator allows users to enter an integrand in order to return the indefinite integral. Does anybody know something about antiderivative solver online? Integral Calculator calculates an antiderivative (indefinite integral) of a function with respect to a given variable using analytical integration. The first thing is the antiderivative you will usually learn, when you begin your study of integral calculus.
As simple we can say, antiderivative finding is the exact opposite process of finding the derivative of any given function. So, before beginning a study of integral calculus, you must have a firm foundation in differential calculus. For an algebraic equation solver, antiderivative finding process is not very complex.
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* Common Factor
* Prime Factor
* Highest Common Factor
Let Us understand About Common Factor
10 = 2 × 5 = 1 × 10
Thus, the factors of 10 are 1, 2, 5 and 10.
15 = 1 × 15 = 3 × 5
Thus, the factors of 15 are 1, 3, 5 and 15.
Clearly, 5 is a factor of both 10 and 15. It is said that 5 is a common factor of 10 and 15. We shall Learn About Prime Factor in our next blog
Subtraction is the operation which finds the difference between the given two numbers. This is also one of the basic operations. There are two terms used in subtraction they are minuend and subtrahend. Where minuend is the term to be subtracted and subtrahend is the term which subtracts the minuend. When the value of the minuend is greatest then the result is positive. When the value of the subtrahend is greatest then the value is negative.
Subtraction Formula:
We shall learn on subtraction formula. The fixed names for the parts of the formula:
c − b = a
Are minuend(c) –subtrahend (b) = difference (a).
As a substitute that c and −b are terms, and subtract as addition of the opposite. The solution is still called the difference.
As a substitute that c and −b are terms, and subtract as addition of the opposite. The solution is still called the difference.
Let us understand with examples
The following problems are simple subtraction.
1) 9 - 9 = 0
The value 6 minus value 6 equal to 0
The solution is 0(zero).
2) 12 – 24 = - 12
The value 12 minus value 24 equal to minus 12
The solution is minus 12
3) 6 – 4 = 2
The value 6 minus value 4 equal to 2
The solution is 2
4) 10 – 7 = 3
The value 10 minus value 7 equal to 3
The solution is 3
5) 5.3 – 1.1 = 4.2
The decimal value 5.3 minus decimal value 1.1 equal to 4.2
A monomial is an algebraic expression in which the only operations that appear between the variables are the product and the power of the natural exponent.
2x2y3z
Parts of a Monomial
Coefficient
The coefficient of a monomial is the number that multiplies the variable(s).
Literal Part
The literal part is constituted by the letters and its exponents.
Degree
The degree of a monomial is the sum of all exponents of the letters or variables.
The degree of 2x2 y3 z is: 2 + 3 + 1 = 6
Similar Monomials
Two monomials are similar when they have the same literal part.
2x2 y3 z is similar to 5x2 y3 z
Degree of a monomial:
The sum of the degrees/exponents of each of the variables in a monomial is called the degree of monomial.
Note: In a non-variable monomial, that is a constant which is any number other than zero, degree is always zero. Like 6, 3, 4, 2 etc. Have a degree zero!
Degree of a Monomial: The degree of a monomial is the sum of the exponents of all its variables. For example, the degree of xy is 2, the degree a^3 b of is 4, the degree of 12 is 0.
Degree of a Polynomial: The degree of a polynomial is the greatest degree of any term in the polynomial. For example, the degree of x^5 - 5x^ 2 is 5, the degree of x^3+y^4-3x^2 = 2y is 4.
Solved Example on Degree
Find the degree of x^8y^6 + x^9 y^6.
Choices:
A. 8
B. 9
C. 16
D. 15
correct answer is d
Solution
Step 1: The degree of a polynomial is the greatest degree of any term in the polynomial.
Step 2: The degree of the second term in x^8y^6 + x^9 y^6 is ‘15’, which is the highest. So, the degree of the given polynomial is 15.
Related Terms for Degree
Monomial
Exponent
Polynomial
Variable
Sum
The degree of a monomial is the sum of the degrees in each of its variables.
The degree of monomial is the sum of the exponents of the variable in the monomial.
The degree of a nonzero constant term is 0.
The constant 0 does not have a degree.
Example: Find the degree of monomial x7y3z2.
Solution: Sum of the degree of in each variables is = 7+3+2 = 12.
Therefore the degree of the monomial is 12.
In our next we shall learn about degree of a polynomial
Algebraic expressionsare formed from variables and constants. We simply use the combination of operations of addition, subtraction, multiplication and division on the variables and constants to form expressions. Algebraic expressions does not contain equal sign.
Some examples of algebraic expressions:
2x + 2y , 2xy , x2 - y2 , 3m + n - 5.
There are one or more terms in the algebraic expressions. For example, 3x2 + 4x + 2 is algebraic expression. It has three terms.
Let us discuss about some example problems on Algebraic expressions.
An algebraic expression is a number, a variable or a combination of the two connected by some mathematical operation like addition, subtraction, multiplication, division, exponents, and/or roots.
For eg.: 4x, 3p, 2a+b, 6z/5
Introduction about Algebraic expressions:
Expressions are a central concept in algebra. A variablecan take various values. Its value is not fixed. On the other hand, a constanthas a fixed value. We combine variables and constants to make algebraic expressions. For this, we use the operations of addition, subtraction, multiplication and division. We have already come across simple algebraic expressions like x + 3, y– 5, 4x + 5, 10y– 5 and so on. The above expressions were obtained by combining variables with constants. We can also obtain expressions by combining variables with themselves or with other variables.In this article we will see some definitions, facts about algebraic expressions
Terms about Algebraic Expressions
Properties about algebraic Expressions:
Like terms: When the terms are same variables then that terms are called as like terms. Otherwise it is called as unlike terms
2xy and 5xy because the factors of 2xy are 2 and x and y. and factors of 5xy are 5 and x and y both factors are same. So these are like terms.
Unlike terms: The terms 2xy and –3x , have different algebraic factors. They are unliketerms. Similarly, the terms, 2xy and 4 are unlike terms. Also, the terms –3x and -4 are unlike term.
Coefficient of the Term: The value in front of the variable is called as the coefficient of the term. The above example the coefficient of x is -3.
Facts about Algebraic Expressions
Monomial: The number of terms in an expression is one then the expression is called as monomial. For example 5x
Binomial:The number of terms in an expression is two then the expression is called as binomial. For example,
x + y, m – 5
Trinomial: The number of terms in an expression is three then the expression is called as trinomial. for example, the expressions x + y + 7, a b + a +b
Polynomial:An expression with one or more terms is called a polynomial. Thus a monomial, a binomial and a trinomial are all polynomials. For Example: 2x3+5x2+15x+22.
Finding the value of an expression:
This is nothing but substituting the values to the variables in the expression. That gives the solution to the expression. For example the area of a square is length2, where l is the length of a side of the square. If l = 8 cm., the area is 82 cm2or 64 cm2; if the side is 12 cm, the area is 122 cm2 or 144 cm2 and so on.
When an expression is written using words or phrases, it is a verbal expression. It is in a statement form. The symbols and statements used have the same meaning as they have in arithmetic.
Signs and symbols:
‘=’ means ‘is equal to’
‘≠’ means ‘is not equal to’
‘<’ means ‘is less than’
‘>’ means ‘is greater than’
‘≤’ means ‘is less than or equal to’
‘≥’ means ‘is greater than or equal to’
The following are the list of words used and their meaning:
1. Addition : sum, plus, add to, more than, increased by, total
2. Subtraction: difference of, minus, subtracted from, less than , decreased by, less
3. Multiplication: product, times, multiply, twice, of
4. Division: quotient , divide, into, ratio
Variable expressions to algebraic expressions:
In Algebra an expression is a term which consists of both symbols and numbers. There are two types in that. They are Algebraic and Verbal expressions. Algebraic expression consists of signs and symbols. The signs involve signs of several operations like addition, subtraction, multiplication and division. The symbol involves all Arabic numerals and literal numbers. Ex: 3ax, 4yz…Verbal expression is the expression which consists of verbal phrases like sum, product, less than, etc…..
Verbal Expressions into Algebraic Expressions Explanation:
Some of the important operations that are used for this verbal expression into algebraic expression are,
In addition with these basic operations some other operations like less than and greater than...
Less than <
Greater than >
Less than or equal <=
Greater than or equal >=
Types of Algebraic Expressions
Monomial
A monomial is an algebraic expression formed by a single term.
Binomial
A binomial is an algebraic expression formed by two terms.
Trinomial
A trinomial is an algebraic expression formed by three terms.
Polynomial
A polynomial is an algebraic expression consists of more than one term.
In math, An algebraic expression is an expression containing symbols, variables and constants together. In math, Verbal expression is a sentence forming from an algebraic expression. Some of the verbal phrases for arithmetic operation is given below. Using these, we can frame the verbal expression for given an algebraic expression.
Let us see brief about verbal expression in math.
Verbal Expression in Math:
The verbal expression for an algebraic expression a + b may write as following,
a plus b , a added to b, a is increased by b, the sum of a and b, b is added to a, b more than a.
The verbal expression for an algebraic expression a - b may write as following,
a minus b , a is decreased by b, b subtracted from a, b less than a, a diminished by b, a reduced by b, the difference between a and b.
The verbal expression for an algebraic expression a x b may write as following,
a times b , the product of a and b, b is multiplied by a.
The verbal expression for an algebraic expression a ÷ b may write as following,
The quotient of a and b, a is divided by b.
Let us learn about how to translate algebraic expression into verbal expression.
Introduction to verbal expression in math:
In math, An algebraic expression is an expression containing symbols, variables and constants together. In math, Verbal expression is a sentence forming from an algebraic expression. Some of the verbal phrases for arithmetic operation is given below. Using these, we can frame the verbal expression for given an algebraic expression.
Let us see brief about verbal expression in math.
Verbal Expression in Math:
The verbal expression for an algebraic expression a + b may write as following,
a plus b , a added to b, a is increased by b, the sum of a and b, b is added to a, b more than a.
The verbal expression for an algebraic expression a - b may write as following,
a minus b , a is decreased by b, b subtracted from a, b less than a, a diminished by b, a reduced by b, the difference between a and b.
The verbal expression for an algebraic expression a x b may write as following,
a times b , the product of a and b, b is multiplied by a.
The verbal expression for an algebraic expression a ÷ b may write as following,
The quotient of a and b, a is divided by b.
Let us learn about how to translate algebraic expression into verbal expression.
Example Problems of Verbal Expression in Math:
Problem 1:
Translate this algebraic expression into verbal expression: 3 + b
Solution:
We can write it as,
b more than 3, 3 plus b, 3 added to b, b is increased by 3.
Problem 2:
Translate this algebraic expression into verbal expression: 3 - b
Solution:
We can write it as,
b less than 3, 3 minus b, b subtracted from 3, b is decreased by 3.
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0.The graph of the quadratic equation is a parabola (either up or down). Let us assume that this parabola has its vertex at (h,k), then we can write the quadratic equation in vertex form as y= a(x-h)2+k.
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