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Algebra 1

Algebra 1. Chapters 7-10. 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.

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Algebra 1

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  1. Algebra 1 Chapters 7-10

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

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

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

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

  6. 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

  7. "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

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

  9. (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

  10. 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

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

  12. 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

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

  14. 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

  15. 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

  16. 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

  17. 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

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

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

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

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

  22. 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

  23. 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

  24.  Solving Proportions •  Percent Problems • Simplifying Rational Expressions • Solving Rational Equations Chapter 11

  25. . • 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

  26. 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

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

  28. Function notation Last Topic

  29. 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 fandx"! Function Notation

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

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