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

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Chapters 7-10

 Graphing  Substitution method  Elimination method  Special cases  System of linear equations

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

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

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

* A "quadratic" is a polynomial that looks like "ax 2 + 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 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.

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

(x 3 )(x 4 ) 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: (x 3 )(x 4 ) = (xxx)(xxxx) = xxxxxxx = x 7

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

Any exponent that is zero is simplified to one.

* 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.

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

* 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

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

* 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.

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.

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

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

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

* Foil is a method of distributing. F IRST O UTER I NNER L AST

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

x 2 + 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.

 Solving Proportions  Percent Problems  Simplifying Rational Expressions  Solving Rational Equations

* 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.

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.)

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

* Function notation

Given f(x) = x 2 + 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"!

* Website used: http://www.purplemath.com/

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