Overview... 3 Chapter : Basic Skills. Order of Operations... 6. lgebraic Epressions... 9.3 Equations.... Simple Linear Equations... 5 Chapter : Sstems of Linear Equations. Graphing Sstems of Linear Equations.... Solving b Substitution....3 Solving b Elimination... 6. Possible Solutions... 3 Chapter 3: naltic Geometr 3. Length of a Line Segment... 36 3. Midpoint of a Line Segment... 39 3.3 Equation of a Circle... 3 3. Medians and Centroids... 5 3.5 Perpendicular Bisectors and Circumcentres... 3.6 ltitudes and Orthocentres... 5 3.7 Classifing ing Shapes... 56 : Polnomials. Epanding and Factoring... 6. Factorization TrinoS tion of Trinomials ()... 66 Chapter : Polnomials.3 Factorization of TSof Trinomials ()... 7. Perfect-square Trinomials and Differences of Squares... 73.5 Factorization Strateg... 77 Chapter 5: Graphs of Quadratic Relations 5. Properties of Quadratic Relations... 5. Finding Zeros... 5.3 Transformations of Quadratic Relations ()... 9 5. Transformations of Quadratic Relations ()... 93 5.5 Modelling Quadratic Relations... 9 Complete MathSmart (Grade ) ISBN: 97--779--
Chapter 6: Solving Quadratic Equations 6. Standard Form to Factored Form... 6. Partial Factoring... 7 6.3 Completing the Square... 6. The Quadratic Formula... 7 6.5 Nature of Roots... 3 Chapter 7: Triangles and Trigonometr 7. Congruent and Similar Triangles... 7. Solving Problems on Similar Triangles... 3 7.3 The Primar Trigonometric Ratios ()... 39 7. The Primar Trigonometric Ratios ()... 7.5 Solving Problems Modelled b Right Triangles... Chapter : cute Triangle Trigonometr. The Sine Law... 5. Solving Problems Using the Sine Law...... 56.3 The Cosine Law......M... 6. Solving Porblems Using the Cosine Law...... 66.5 ppling the Sine Law and the Cosine Law... 7 iew... M... Cumulative Review... 77 Hand Reference... 9 nswers......ṡ... 97 ISBN: 97--779-- Complete MathSmart (Grade ) 5
5 Graphs of Quadratic Relations Parabola: a graph of a quadratic relation that is shaped like the letter U is of smmetr: a line that divides a parabola into two equal halves Verte: the highest or lowest point of a parabola 5. Properties of Quadratic Relations Identif and check the representations of quadratic relations. - - - - - - -3 5 3 5 7 9 second differences are constant but not shows a parabola - - 59-5 59 Parabola -intercept -intercept C E opens upward verte ais of smmetr 5 - - - - B D F Graph the quadratic relations. = B = - + - - - - - - - - - - - - Complete MathSmart (Grade ) ISBN: 97--779--
Graph the quadratic relations. Write the ke characteristics of each in the table. C = D = - + + - - - - - - - - - - -intercept(s) - - E = - ( ) F = ( + ) + - - - - -3 - - - = = - + + = - ( ) = ( + ) + (, )(, ) 6 - - = - - -intercept (, ) Direction of Opening is of Smmetr = Verte (, ) Ma./Min. Value = ISBN: 97--779-- Complete MathSmart (Grade )
Chapter 5 Graphs of Quadratic Relations Sketch the parabolas with the given characteristics. G verte: (-3,) -intercept: (,) B B -intercept: (.5,) -intercept: (,-6) C D nswer the questions without graphing. H = + 7 no -intercepts opens upward -intercepts: (,), (-,) ma. value: 3 a. What is the direction of opening? os b. What is the -intercept? I = 6 + 63 a. What is the direction of opening? C D Standard Form of Quadratic Relations = a + b + c direction of opening a >, upward a <, downward (,) -intercept e.g. = + = - + (,) b. Will there be a maimum value or a minimum value? J = -( ) Epand and rewrite in the form: = a + b + c. a. What is the direction of opening? b. What is the -intercept? Complete MathSmart (Grade ) ISBN: 97--779--
Circle T for true and F for false. K The ais of smmetr is alwas the -ais. L The verte alwas lies on the ais of smmetr. M parabola with no -intercepts and with a positive -intercept alwas opens upward. N ll parabolas have -intercepts. O Consider = a + b + c. Stud each scenario and answer the questions. P Q a. If it is an equation of a parabola, then a cannot be. b. If a is negative, the parabola will open downward. c. c is the -intercept. The graph shows the path made b Steven s dive. a. Check the equation that represents the graph where represents the horizontal distance and represents the water depth. + MP =. + B =. C = -. b. What was the maimum water depth Steven reached? The graph shows the water arch Karen s garden hose made while she watered her plants. a. Check the equation that represents the graph where represents the horizontal distance and represents the height. = + 5 B = -.5 C = -.6 +.7 +.5 b. How far awa was Karen from the plants? ISBN: 97--779-- Complete MathSmart (Grade ) 3