Algebra 1 Chapters 7-10

Chapter 7 Graphing Substitution method Elimination method Special cases System of linear equations Chapter 7

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

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

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

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. Special cases

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. System of Linear equations

Chapter 8 Add multiply & subtract exponents Negative exponent Exponent of zero Scientific notation Chapter 8

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 Add multiply & subtract 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 Negative exponents

Any exponent that is zero is simplified to one. Exponent of zero

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. Scientific Notation

Chapter 9 Square roots Graphing inequalities Solve by taking the square root Graphing quadratic equations (vertex) Quadratic formula Discriminant Chapter 9

Square root of 25 = 5 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 Square Roots

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

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. Solve by taking square roots

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. Graphing Quadratic Equations

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

The discriminant b²-4ac A function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial. b²-4ac The discriminant

Chapter 10 Adding and subtracting polynomials Multiplying- distributive Property and FOIL method              Special case - Factoring solve by factoring factoring trinomials a=0 - Chapter 10

Foil is a method of distributing. FIRST OUTER INNER LAST FOIL

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. Adding and subtracting Polynomials

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. Solve by factoring

Chapter 11 Solving Proportions Percent Problems Simplifying Rational Expressions Solving Rational Equations     Chapter 11

. Cross multiply and simplify if you can. Reduce your answer if possible. 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.  5(2x + 1)  =  2(x + 2)  10x + 5  =  2x + 4  8x  =  –1  x = –1/8 Solving Proportions

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.) Percent's

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

Function notation Last Topic  

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"! Function Notation

By Kiara Eisenhower Website used: http://www.purplemath.com/