Chapters 7-10. Graphing Substitution method Elimination method Special cases System of linear...

Chapters 7-10

*Algebra 1

*Chapter 7

Graphing

Substitution method

Elimination method

Special cases

System of linear equations

*Graphing

You have to type the system into the y= screen on the calculator.

*Substitution method

After you find the value you have to plug the answer into the other equation.

*Elimination method

Type in the Y= screen on the calculator and graph and find where the two lines intersect.

*Special cases

*A "quadratic" is a polynomial that looks like "ax2 + bx + c", where "a", "b", and "c" are just numbers. For the easy case of factoring, you will find two numbers that will not only multiply to equal the constant term "c", but also add up to equal "b", the coefficient on the x-term.

*System of Linear equations

*"system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.

*Chapter 8

Add multiply & subtract exponents

Negative exponent

Exponent of zero

Scientific notation

*Add multiply & subtract

exponents

(x3)(x4)   To simplify this, I can think in terms of what those exponents mean. "To the third" means "multiplying three copies" and "to the fourth" means "multiplying four copies". Using this fact, I can "expand" the two factors, and then work backwards to the simplified form:(x3)(x4) = (xxx)(xxxx)

          = xxxxxxx           = x7

*Negative exponents

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side of the line. * flip the line change the sign

*Exponent of zero

Any exponent that is zero is simplified to one.

*Scientific Notation

*I need to move the decimal point from the end of the number toward the beginning of the number, but I must move it in steps of three decimal places.

*Chapter 9

Square roots

Solve by taking the square root

Quadratic formula

Graphing quadratic equations (vertex)

Discriminant

Graphing inequalities

*Square Roots

*Roots are the opposite operation of applying exponents. For instance, if you square 2, you get 4, and if you take the square root of 4, you get 2. if you square 3, you get 9, and if you take the square root of 9, you get 3:

Square root of 25 = 5

*Graphing Inequality's

*remember to flip the inequality sign whenever you multiplied or divided through by a negative (as you would when solving something like –2x < 4.

*Solve by taking square roots

*When solving by square roots you first need to have the variable on one side then once you do you can solve by square rooting. You should square root the number by positive and negative.

*Graphing Quadratic Equations

You would type the equation in the y= screen and then see the graph chart that will show you the x and y values that you plot. You would connect your parabola and then shade under or below depending on you inequality symbol.

*Quadratic formula

*The Quadratic Formula: For ax2 + bx + c = 0, is put into this formula

*The discriminant

*A function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial.

b²-4ac

*Chapter 10

Adding and subtracting polynomials

Multiplying- distributive Property and FOIL method           

Special case - Factoring

factoring trinomials a=0 -

solve by factoring

*FOIL

*Foil is a method of distributing.

FIRST

OUTER

INNER

LAST

*Adding and subtracting Polynomials

When adding polynomials all you do is combine like terms. When subtracting you must first distribute the negative number in front of the parentheses.

*Solve by factoring

x2 + 5x + 6 = 0

(x+2) (x+3) * set this equal to zero

(x+2) (x+3) = 0

-2 -3 * then do the opposites

First you need to make sure your equation is in standard form. Then you want to factor out the equation, then set it to zero then write out the opposite.

*Chapter 11

 Solving Proportions

 Percent Problems

Simplifying Rational Expressions

Solving Rational Equations   

*Solving Proportions

*Cross multiply and simplify if you can. Reduce your answer if possible.

.

5(2x + 1)  =  2(x + 2) 10x + 5  =  2x + 4 8x  =  –1 x = –1/8

Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross multiplying, and solving the resulting equation. 

*Percent's

Decimal-to-percent conversions are simple: just move the decimal point two places to the right. 

0.23 = 23% 2.34 = 234% 

0.0097 = 0.97%

*(Note that 0.97% is less than one percent. It should not be confused with 97%, which is 0.97 as a decimal.)

*Simplifying rational

expressions

*The only common factor here is "x + 3", so I'll cancel that off. Then the simplified form is

*Last Topic  

*Function notation

*Function Notation

Given  f(x) = x2 + 2x – 1, find  f(2)

(2)2 +2(2) – 1        = 4 + 4 – 1        = 7

While parentheses have, up until now, always indicated multiplication, the parentheses do not indicate multiplication in function notation. The expression "f(x)" means "plug a value for x into a formula f "; the expression does not mean "multiply fand x"!

*By Kiara Eisenhower

*Website used:

http://www.purplemath.com/