A) Solve the linear system.

y=2x+4 and x+2y=12 1) y=2x+4 is solved

x+1(2x+4)=12 2) Put 2x+4 for y

4x+8=12 3) Subtract 8

-8 -8

4x=4 4) Divide by 5

x= 1

Chapter 10 Worked Out Examples

1) Find the zero of the function

f(x) = x (squared) - x - 12

0= x (squared) - x - 12

0= (x+12)(x-1)

x= -12 or 1

2) f(x) = x (squared) + 4x - 5

0= x (squared) + 4x - 5

0= (x+5)(x-1)

x= -5 or 1

Chapter 11 Worked Out Examples

1) (The square root of) 25

first you factor it

5x5 which is a perfect square

5

2) Find the unknown length

a= 3, c= 5

3 (squared) + b = 5 (squared)

9 + b = 25

-9 -9

b= 16 (squared)

Chapter 6 Worked out examples

Solve the Ineqaulity

A)

2x-3>7 1) Add 3 to both

+3 +3 sides.

2x>10 2) Dived each side 2x/2 10/2 by 2.

x>5 3) Then you get B) your finale answer.

4-2m>7-3m 1) Add 3m to both

+3m +3m sides.

4+m>7 2) Subtract 4 from

-4 -4 both sides.

m>3 3) Then you get your

finale answer.

Chapter 8 Worked Out Example

A) Simplify

4(squared) x 4(to the 6 power)

Add them together 1) add

4(to the 8 power) 2) your final answer

B) 3(cubed) x 3

add them together 1) add

3(to the 4 power) 2) your final answer

**Algebra 1 Final Exam Review Project**

Important Ideas

In an inequality problem, if you multiply or divide a negative you must flip the sign.

Example: > becomes <

When graphing inequalities the signs make your mark on the graph different. Ex: > or < would be a open circle where as < > would be a filled circle.

Explanation

Explanation

Exponents are usually easy for me i just wanted some examples. These taught you how to simplify your exponents which is very important.

Explanation

The square root was a one of the more troubling aspects of algebra. Its quite difficult when it's not a perfect square. That' why I felt the need to put these examples.

Word definitions

Inequality- A mathmatical sentence formed by placing one of the symbols <, >, or the greater than or equal to one. Also the lesser than or equal to on, between two expressions.

Equivalent Inequalities- Inequalities that have the same solutions.

Word Definitions

System Of Linear Equations- Two or more linear equations in the same variables; also called a linear system.

Inconsistent system- A linear system with no solution. The graphs of the equation with an inconsistent system are parallel lines.

Importan Ideas

1) In the activity, you saw what happens when you raise a number to a zero or a negative exponent. The activity sugests the following defenitions.

a to the 0 power is 1

a to -n is the reciprocal of a to n

a to n is the reciprocal of a o -n

2) Numbers such as 1,000,000, 153,000, and 0.00009 are written in standard form. Another way to write a numer i to use scientific notation.

Important Ideas

1) A radical expression is in the simplist form if the following conditions are true:

- No perfect squae factors other than 1

are in the radicand

- No fractions are in th radicnd

- No rdicals apear in the denominator of

a fraction

2) An equation that contains a radical expression with a variable in the radiand is a radical equation.

3) a (squared) + b (squared) = c (squared)

Explanation

I've always struggled with quadratic functions and quadratioc quations. So I decided to put some in for extra practice and some examples.

Important Ideas

A quadratic function is a nolinear function that can be written in the standard form y=ax (squared) +bx+c where a =/= 0. Every quadratic function has a U-shaped graph called a parabola.

A standard equation is an equation that can be written in the standard form

ax(squared) + bx + c = 0

Chapter 9 Worked Out Example

1) (6n (squared) + 5) + (n (squared) +2n - 4)

(6n (squared) + 5)

+ (n (squared) + 2n - 4) 1) Add them together

9n (squared) + 1

2) Factor the trinomial

Z (squared) + 8z - 48 1) Find the factors

12 and (-4) 2) The sum is 8

12 + (-4) = 8

Z (squared) + 8z - 48 = (z+12)(z-4)

Explanation

These problems are usually easy but the farther you go into the chapters the harder they get. They can get super hard actually if you go further into the chapter.

Important Ideas

1) F irst

O utside

I nside

L ast

2) For real numbers a and b, if a=0 or b=0 then, then ab=0.

Explanations for A and B.

A and B) When we first started the chapter figuring out ineqaulities was a big struggle for me. I didn't understand how to figure out the problems till Mrs.Gilis explained it.

Important Ideas

1) Whe solving a linear system,you can sometimes add or subtract the equations to obtain a new equation in one variable. This method is called elimination.

2) A system linear equation, or simply a linear system, comsists of two or more inear eaquations witht the same variables.

Definitions

Scientific Notation- A number is written in scientific notation when it is of the form c x 10 to n where 1< c <10 and n is an integer.

Definitions

Roots- The solutions of an equation in which one side is zero and the other side is a product of a polynomial factors.

Zero Of A Function- An x-value for which f(x)=0 (or y=0)

Definitions

Quadratic Function- A nonlinear function that can be written in the standard form y=x(squared) + bx + c

Parabola- The U-shaped grapgh of the quadratic function.

Axis of Symmetry- The line that passes through the vertex and divides the parabola into two symmetric parts.

Parent Quadratic function- The funcion

f(x)= x, which is the most basic function in the family of linear functions.

Definitions

Radical equation- An equation that contains a radical with a variable in the radicand.

Extraneous solutions- A solution of a treansformed equation that is not a solution of the original equation.

Radical expression- An expression that contains a radical, such as a square root, cube root, or other root.

Radical function- A function that contains a radical expression with the independent variable in the radicand.

I never really got linear equations. they have always been really confusing. Now I have practiced them more I understand them.