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Algebra

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Parabola

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Parabolas and their functions

Parabolas 1.Normal Parabola f(x) = x? root : (0/0) apex : deepest point/highest point of the parabola 2.Displacement up/down the y-axis f(x) = x?+k root : 1 solution: k = 0 2 solutions: k > 0 0 soltuions: k < 0 apex : (0/k) 3.Displacement on the x-axis f(x) = (x + h)? root = apex : (-h/0) 4. Displacement on x- and y-axis f(x) = a(x+h)? + e root : look at 2. aspex : (-h/k)
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Pythagorean Theorem

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This formula is extremely essential especially later on. Note that this formula only applies to right triangles.  The formula is

a^2+b^2=c^2

A and B being the two legs.

C being the hypotenuse of the triangle.

The hypotenuse (c) is the side opposite the largest angle in the triangle.  In this case for a right triangle, the hypotenuse will always be opposite of the right angle.

Junior Math League Competition

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The following are the 2 problems from the NVCM math league contest. The answers will be provided at the bottom. Note: This requires knowledge and use of both geometry and algebra. Also " means the same as the previous equation. 1. The difference between two consecutive perfect squares is 739. Write the larger of these perfect squares. Solution: Let x^2 be the larger and (x-1)^2 be the smaller of the two squares. Then 739= x^2-(x-1)^2 "=x^2-(x^2-2x+1) "=2x-1 740=2x 370=x You must find the larger which is represented by x^2 so---- x^2 370^2 136,900---- Answer 2. The product of two positive, consecutive odd integers is 4623. Find the smaller integer. Solution:

Algebra

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Use FOIL to help solving math problems. It means FIRST OUTSIDE INSIDE LAST. Also the website www.algebra.com will help
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Algebra notes

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Lauren Gruffi 11/3/10 Italian III Study Guide -are conjugation: o, i, a, iamo, ate, ano -ere conjugation: o, i, e, iamo, ete, ono -ire conjugation: o, i, e, iamo, ite, ono -care/gare: o, hi, a, hiamo, ate, ano -ciare/gare: comincio, cominci, comincia, cominciamo, cominciate, cominciano Irregular Verbs: - Bere: bevo, bevi, beve, beviamo, bevete, bevano - Dire: dico, dici, dice, diciamo, dite, dicono - Dare: do, dai, da, diamo, date, danno -Know modal verbs: dovere, potere, e volere Ex: Posso venire anch?io? Avere expressions: Avere vergogna ? to be shameful Avere voglia di ? to feel like Avere pazienza ? to have patience Avere sonno ? to be sleepy Fare expressions: Fare una passeggiata ? to take a walk

Exponents

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? ? mptii menu THE UNIVERSITY OF AKRON Mathematics and Computer Science Lesson 2: Exponents & Radicals Directory ? Table of Contents ? Begin Lesson 2 A n Al geb ra Review I amDPS N ? Z ? Q ? R ? C a 3 a 4 = a 7 (ab) 10 = a 10 b 10 ?(ab? (3ab? 4)) = 2ab? 4 (ab) 3 (a ?1 + b ?1 ) = (ab) 2 (a + b) (a? b) 3 = a 3 ? 3a 2 b + 3ab 2 ? b 3 2x 2 ? 3x? 2 = (2x + 1)(x? 2) 1 2 x + 13 = 0 =? x = ?26 G = { (x, y) | y = f(x) } f(x) = mx + b y = sinx in Ten Lesso ns Copyright c ?1995?2000 D. P. Story Last Revision Date: 2/2/2000 Lesson 2: Exponents & Radicals Table of Contents 2. Exponents and Radicals 2.1. Integer Exponents 2.2. The Law of Exponents ? How to Multiply or Divide Two Powers ? How to Calcu-

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