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Elementary mathematics

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

Geometry TN 2018 2019 Curriculum Map Q1

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Curriculum and Instruction ? Mathematics Quarter 1 Geometry Mathematics Geometry: Year at a Glance 2018 - 2019 Aug. 6 ? Oct. 5 Oct. 16 - Dec. 19 Jan. 7 ? Mar. 8 Mar. 18 ? May 24 TN Ready Testing Apr. 22 - May23 Tools of Geometry, Reasoning and Proof, Transformations and Congruence, Transformations and Symmetry, Lines and Angles Triangle Congruence with Applications, Properties of Triangles, Special Segments in Triangles, Properties of Quadrilaterals with Coordinate Proofs Similarity and Transformations, Using Similar Triangles, Trigonometry with Right Triangles, Trigonometry with All

Note Taking Guide 1.1

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Numerical Operations Essential Questions After completing this lesson, you will be able to answer the following questions: How are expressions rewritten in simplified form based on the mathematical operations in the expression? What is the correct order for performing mathematical operations in simplifying expressions? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Real Numbers(P.1) Natural Number: _______________ integers ____________ Numbers: A member of the set of positive integers or zero Integers: A number that can be written without a fraction or _______________ Rational Numbers: Can include positive/negative fractions and decimals. Irrational Number: Any real number that can not be expressed as a ratio. Adding and Subtracting Integers(P.2)

Basic Aglebra

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Basics of Algebra Algebra is a division of mathematics designed to help solve certain types of problems quicker and easier. Algebra is based on the concept of unknown values called variables, unlike arithmetic which is based entirely on known number values. This lesson introduces an important algebraic concept known as the Equation. The idea is that an equation represents a scale such as the one shown on the right. Instead of keeping the scale balanced with weights, numbers, or constants are used. These numbers are called constants because they constantly have the same value. For example the number 47 always represents 47 units or 47 multiplied by an unknown number. It never represents another value.

Algebra Sin, Cos, and Tan

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A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question. In any right angled triangle, for any angle: The sine of the angle = the length of the opposite side the length of the hypotenuse The cosine of the angle = the length of the adjacent side the length of the hypotenuse The tangent of the angle = the length of the opposite side the length of the adjacent side So in shorthand notation:

Trigonometric Functions

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In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

Extra Practice Problems for Sequence/Series

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1. Tell whether each sequence is arithmetic, geometric, or neither. a. 1, 5, 9, 13, . . . b. 2, 6, 18, 54, . . . c. 1, 1, 2, 3, 5, 8, . . . d. 16, 4, 1, 0.25, . . . e. ?1, 1, ?1, 1, . . . f. 5.6, 2.8, 0, ?2.8, . . . 2. Find the common difference, d, for each arithmetic sequence and the common ratio, r, for each geometric sequence. a. 6, 11, 16, 21, . . . b. 100, 10, 1, 0.1, . . . c. 1.5, 1.0, 0.5, 0, ?0.5, . . . d. 0.0625, 0.125, 0.25, . . . e. ?1, 0.2, ?0.04, 0.008, . . . f. ?4, ?3.99, ?3.98, . . . 3. Write the first six terms of each sequence, starting with u1. a. u1 ? ?18 b. u1 ? 0.5 un ? un?1 ? 6 where n ? 2 un ? 3un?1 where n ? 2 c. u1 ? 35.6 d. u1 ? 8 un ? un?1 ? 4.2 where n ? 2 4. Write a recursive formula to generate each sequence. Then find the indicated term.
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