Indiana Jones Math
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Mathematics
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Precalculus - Function (Difference Quotient)
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AP Calculus - Limits, Derivatives, and Integrals.
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Calculus Textbook UBC
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Apcs solution acsl
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American Computer Science League Flyer Solutions 1. Boolean Algebra )( BA? CBBA ?( ) = BA CBBA ?( ) = 000 ???? CBBABAA 2. Computer Number Systems 18 = 1, 1002 = 4, 118 = 9, 1016 = 16 so the sequence is 1, 4, 9, 16 ? n2 . The 10th term is 102 = 100 = 1448 3. LISP (EXP (DIV (MULT (ADD 2 (SUB 4 2 ) ) 3 ) 2 ) 4 ) = (EXP (DIV (MULT (ADD 2 2 ) 3 ) 2 ) 4 ) = (EXP (DIV (MULT 4 3 ) 2 ) 4 ) = (EXP (DIV 12 2 ) 4 ) = (EXP 6 4 ) = 1296 4. Prefix/Infix/Postfix 4 3 + 7 5 - * 2 ^ = (4 + 3) (7 - 5) * 2 ^ = 7 * 2 2 ^ = 14 ^ 2 = 196 5. Bit String Flicking (LCIRC-3 (RSHIFT-2 X)) = 10001 Let X = abcde RSHIFT-2 abcde = 00abc LCIRC-3 00abc = bc00a bc00a = 10001 b = 1, c = 0, a = 1, d = * and e = *
quadratic formula notes
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Section 4-6: The Quadratic Formula and the Discriminant The standard form of a quadratic is: +('' The quadratic formula is: )(. - - , where a, b, and c are real numbers where a # 0. - > What is the purpose of using the quadratic formula? : / What is the expression used to find the discriminant: \ > What information does the discriminant tell you? / (IC IS Value of Discriminant: ( Number and types of 'I \ ( solutions: Graph will look like: Find the discriminant of the quadratic equation and give the number and type of solutions of the equation. Ex 1) a. x2 +6x+11 b.x2 +6x+9 c.x2 +6x+5 1 - - L - Identify the discrimant of-eacb of-the following equations and state how many solutions and what
completing the square examples
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Ex 2: f(x)= 7x2 +28x+56 o X1-F4(tsl' - - ? 510 71-J 2 +q)c -- (9'' H 84- x L +Lfx+ i F-4 = F( T *?g J?Z t r?q - = )C+z H Fx ?2? j Section 4-5: Solving with Completing the Square The Process 1) Set equation 0 2) Shove the constants to the other side 3) Get the Leading Coefficient to be 1 4) Complete the Square. Then add that value to both sides. 5) Take the square root of both sides and solve for x. For Examples 1-5 Find the solutions to the quadratic. Ex 1: f(x) = 3x2 + 42x + 24 0 3tL) 4- 2 ( - _ +r~ X Ex 3: g(x)=6x2 +6x+12 0 ('x 2. +LocW - xt / \ 1.- 2. - :+? - 9 '4 ( / X OL 0 Section 4-5: Solving with Completing the Square Ex4:y=x2 +7x+2 Ex5:f(x)=3x2 -12x+l O3x/yl
completing the square
Subject:
Section 4.5: Vertex form with Completing the Square Completing the Square: Used to change quadratic functions in standard form to vertex form. f (x) = ax 2 + bx + c - f(x)=a(x?h) 2 +k ------------------------ Investigation This creates a Perfect Square 2 (b)2 Tririomiai, which factors To complete the square for an expression x + bx, add ------ Startwithx2 + bx Find (b)2 x2 +bx+() (x+ )2 / The Completed Square Factored form x2 +6x - x2 +4x 2 X - 8x _) - X - 2x oF W4CX 1rrrt! You Try?Complete the Square for the following. Then write the factored form. 1)x2 +14x 2)y2 +20y 2t\2S io) IOD (xiiJJ _ 0) 3)m2 -IOM L Omtn - 15 ) ;4 6 7 4)h2 -15h '4 P7 L_'1-' & ? **How do we go from standard form of mAquation to vertex form?
graph quadratics in vertex form
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3 H 5 Vt4Section 4.7: Graph of Quadratic Functions in Vertex or Intercept rm. J *Reca ll the transformations from Section 2.7 we learned f(x) = a I x - hi + Ic for absolute value functions. Vertex Form of a Quadratic f(x) =' (x - h)2 + ? Vertex: -Kit itc'1eS-- 0 r 2f4oO&1 Axis of Symmetry: In 0 *l.L tot,&) J'&H- ? Opens up/down if: Example 1: Given f(x) = x2, write it in vertex form and graph. totAJe-k- polv1+ on hne con1-aiw\k -' 4?LiOOlO?' j x ' - t 03 I \ z_ (oo) h t. Example 2: Given f(x) = (x - 3)2 - 5, state the vertex and axis of symmetry, describe the translations, and graph. (h,-) Vertex: (y) Axis of Symm: 3 Translations: 110flZ0iT1t'A 1 (C\\* 3 \rc&k C1$SIO(\ Vi (extjj \- CoLJJfl .iej~ 5o~ I ~~ k q I
square roots and imaginary numbers
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?6= ?2 b) 25 c) 7(x-4)2 ?18=10 tt fS )c 100 - f(TI1)jii Solving Quadratic Equations by Finding Square Roots Objective: To solve quadratic equations with real solutions. If R2=S, then Risa (00+ of S. A positive number S has 2 square roots written as ( and . ?O Properties: Product Property: V'-a- Quotient Property:Tb Simplify the expression (radical) a) b) c) id * 1-5 Rationalize Denominators of fractions 1 1 5D re: a, / 1,0 a) J ~S? I- b) 2 rOL - I Steps to solving quadratic equations: Step 1: Write the original equation - V+3f 1:-- ?4 } d) I? '- V64 '4L.f Form of the denominator Multiply numerator and denominator by: (multiply the _by_ _conjugate) puC 3 - j --3)-2 i_i0 (7+) ?- F (p
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