High school algebra 2 help

Introduction to algebra 2:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.                        (Source: Wikipedia)

In this article we shall learn about the concepts of algebra for high school with examples . Algebra for high school includes topics on rules of operations and relations, polynomials, equations, numerical structures etc

We will work out some examples from high school algebra.

Topics under algebra 2:

Quadratic equation
Linear equation
Non linear equation
Factorization

Chapters for algebra 2 high school:-

• Equations and Inequalities

• Linear Relationships and Functions

• Systems of Linear Equations and Inequalities

• Matrices and Matrix Operations

• Quadratic Equations

• Polynomial Functions

• Rational Expressions, Equations and Exponents

• Exponential and Logarithmic Functions

• Sequences and Series

• Trigonometry

• Trigonometric Identities and Graphs and Formulas

• Quadratic Relations/Analytic Geometry.

Example algebra 2 high school problems:-

Algebra 2 high school problem1:-

Find the minimum and maximum siginificant of the function f(x, y) = 4x + 3y, if the vertices are (–1, 3), (3, 5), (4, –1) and (–1, –2).

Solution:-

Recall where the maxima and minima can occur.

Step 1

Maxima and minima can only occur at the vertices.

Substitute the coordinates of the vertices into the function, f(x, y) = 4x + 3y.

Step 2

Substitute the coordinates of the vertices into the function, f(x, y) = 4x + 3y.

Algebra 2 high school problem1

Find the maximum and minimum values from the table.

Step 3

From the above table, we find that the maximum value of the function is:

f(3, 5) = 27

And the minimum value of the function is: f(–1, –2) = –10.

Algebra 2 high school problem2:-

Solve using square roots:

3x2 = 75

Solution:-

Divide by 3.

Step 1

Dividing both sides by 3:

X2=25

Take the square root.

Step 2

X=`+-` 5

Taking the square root on both sides of the equation:

Algebra 2 high school problem3:-

Check whether 4x + 1 are a polynomial or not. Write along its degree and coefficient if it is a polynomial and if it is not a polynomial, clarify why not.

Solution:-

Use the definition of the polynomial.

Step 1

The expression 4x + 1 is of the form:

anxn + an – 1xn – 1 + an – 2xn – 2 + .....a1x1 + a0

where n is a positive integer and an`!=` 0.

Thus, it represents a polynomial.

Find the highest exponent of the given expression.

Step 2

The highest exponent of the given expression is 1.

Thus, the polynomial has degree 1.

Find the coefficient of the highest degree term.

Step 3

The coefficient of the highest degree term is 4.

Thus, the leading coefficient is 4.

High school algebra 2 help example 1:

Find the values of x for the given quadratic function x2 - 4x - 12 = 0.

Solution:

Given function is x2 - 4x - 12 = 0

First we find the sum of two numbers is (- 4x) and its product is - 12x2. The two numbers are (- 6x, 4x).

x2 - 4x - 12 = 0

x2 - 6x + 4x - 12 = 0

Grouping the first two terms and second two terms, we get

(x2 - 6x) + (4x - 12) = 0

Take common terms, we get

x (x - 6) + 2 (x - 6) = 0

(x - 6) (x + 2) = 0

The factors are (x - 6) and (x + 2)

Equate the factors to zero, we get

x = 6, x = - 2

Answer:

The final answer is x = 6, - 2

High school algebra 2 help example 2:

Solve the linear equations x - 4y = 10 and 2x + 4y = 80

Solution:

The given linear equations are x - 4y = 10 and 2x + 4y = 80

Add the given two equations, we get

3x = 90

Divide by 3 on both the sides, we get

x = 30

Substitute the value of x in the first equation, we get

30 - 4y = 10

Subtract by 30 on both the sides, we get

- 4y = - 20

Divide by - 4 on both the sides, we get

y = 5

Answer:

The final answer is x = 30, y = 5

Practice problems for high school algebra 2 help

High school algebra 2 help example 1:

Find the factors values of the given quadratic function x2 + 35x + 174 = 0.

Answer:

The factors are (x + 29) (x + 6)

High school algebra 2 help example 2:

Find the factors values of the given quadratic function x2 - 40x - 375 = 0.

Answer:

The factors are (x - 25) (x - 15)

High school algebra 2 help example 3:

Solve the given linear equation and find its solution x + 7y = 38, 18x - 2y = 44

Answer:

The final answer is x = 3, y = 5