Lesson 5.3 Exercises, pages

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1 Lesson 5.3 Eercises, pages 37 3 A. Determine whether each ordered pair is a solution of the quadratic inequalit: 3 - a) (-3, ) b) (, 5) Substitute each ordered pair in» 3. L.S. ; R.S.: 3( 3) 3 L.S. 5; R.S.: 3() Since <3, the ordered pair Since 5>, the ordered pair is not a solution. is a solution. c) (, ) d) (-5, 1) L.S. ; R.S.: 3() L.S. 1; R.S.: 3( 5) 71 Since, the ordered pair Since 1<71, the ordered is a solution. pair is not a solution. 5. Match each inequalit with a graph below. i) 6 ( + 1) - ii) ( - ) - 1 iii) 7 ( - 1) + iv) ( - ) + 1 a) b) 6 The parabola is congruent to The parabola is congruent to, and its verte is (1, )., and its verte is (, 1). ( 1) ( ) 1 The inequalit is: The inequalit is: >( 1) ( ) 1 17

2 c) d) 3 The parabola is congruent to The parabola is congruent to, and its verte is ( 1, )., and its verte is (, 1). ( 1) ( ) 1 The inequalit is: The inequalit is: <( 1)» ( ) 1 6. Write an inequalit to describe each graph. a) b) 1 1 All parabolas are congruent to, and have verte (, ). The equation is: The curve is solid and The curve is broken and the the shaded region is below. shaded region is above. An inequalit is: An inequalit is: > c) d) 1 1 The curve is solid and The curve is broken and the the shaded region is above. shaded region is below. An inequalit is:» An inequalit is: < 1 DO NOT COPY. P

B 7. Graph each inequalit. Write the coordinates of 3 points that satisf the inequalit. a) < - + The graph of the related quadratic function is congruent to and has verte (, ).

3 points that satisf the inequalit have coordinates: (1, ), (, 1), ( 1, 1) b) ( + ) The graph of the related quadratic function is congruent to and has verte (, ).

3 B 7. Graph each inequalit. Write the coordinates of 3 points that satisf the inequalit. a) < - + The graph of the related quadratic function is congruent to and has verte (, ). The curve is broken and the region below is shaded. 3 points that satisf the inequalit have coordinates: (1, ), (, 1), ( 1, 1) b) ( + ) The graph of the related quadratic function is congruent to and has verte (, ). The curve is solid and the region above is shaded. 3 points that satisf the inequalit have coordinates: (, ), ( 1, 3), (, 5) c) ( - 1) + 5 The graph of the related quadratic function is congruent to and has verte (1, 5). The curve is solid and the region below is shaded. 3 points that satisf the inequalit have coordinates: ( 1, ), (1, ), (, ) 6 Graph of 6 Graph of ( ) Graph of ( 1) 5. Are the points on the graph of = part of the solution of the inequalit > ? Eplain our answer. No, the points are not part of the solution, because the inequalit indicates that is greater than 3 7, and, on the line, Use technolog to graph each inequalit. Sketch or print the graph. a) b) > Graph the related quadratic functions. The boundar is part of The boundar is not part of the graph. the graph. 19

4 1. Graph each inequalit. Write the coordinates of 3 points that satisf the inequalit. a) b) > Graph of 6 1 Graph of Complete the square for: Complete the square for: ( ) 5 ( 3) 1 ( ) 3 The graph of this function The graph of this function is congruent to and is congruent to and has verte ( 3, 1). has verte (, 3). The curve is solid and the The curve is broken and the region below is shaded. region above is shaded. 3 points that satisf the 3 points that satisf the inequalit have inequalit have coordinates: (, 1), (, 1), coordinates: (1, ), (, ), (, 3) (3, 1) 11. Write an inequalit to describe each graph. a) b) 1 16 The parabola is congruent to The parabola is congruent to, and has verte 3, and has verte (, ). (, 3). ( ) 3( ) 3 The curve is solid and the The curve is broken and the region below it is shaded. region above it is shaded. An inequalit is: An inequalit is: ( ) >3( ) 3 DO NOT COPY. P

5 1. a) For A(-1, a) to be a solution of > - + 5, what must be true about a? In > 5, substitute: 1, a a> ( 1) 5 a>3 b) For B(b, 6) to be a solution of > - 5, what must be true about b? In > 5, substitute: b, 6 6>b 5 b <11 b< 11 or b> 11 That is, 11<b< Two numbers are related in this wa: three times the square of one number is greater than or equal to the other number minus. a) Graph an inequalit that represents this relationship. Let the numbers be represented b and. An inequalit is: 3», or 3 The graph of the related function is congruent to = 3 and its verte is (, ). The curve is solid, with the region below it shaded. Graph of b) Use the graph to list three pairs of integer values for the two numbers. Three pairs of integer values are: (, 16), ( 1, ), (1, 1) 1. Graph this quadratic inequalit: ( + 1) - 3 > 3 ( 1) 3> Multipl b ( 1) 3(3)> <1.5( 1) 9 The graph of the related function is congruent to 1.5 and its verte is ( 1, 9). The curve is broken, with the region below it shaded. Graph of 1.5( 1) 9 1

15. An arch that supports a bridge over a river is parabolic and spans a horizontal distance of 5 m. An equation of the parabola is =-. + 1.

6 15. An arch that supports a bridge over a river is parabolic and spans a horizontal distance of 5 m. An equation of the parabola is = ,where metres is the height of a point on the arch above the river, and metres is the horizontal distance to that point measured from one end of the arch. a) Write an inequalit to represent the cross-sectional region between the arch and the river. Since both and are positive, the graph of the parabola is onl in Quadrant 1. An inequalit is: <. 1., >, > b) Graph the inequalit, then sketch it below. Use a graphing calculator. Graph. 1., >, > in Quadrant 1 with a broken curve. Shade the region between the curve and the -ais. c) The tallest mast of a ship is 37 m above water level. Can the ship pass under the arch when it is 5 m from one end of the arch? Justif our answer. Check whether the point (5, 37) satisfies the inequalit. In <. 1., substitute: 5, 37 L.S. 37 R.S.:.(5) 1.(5) Since L.S.<R.S., the ship can pass under the arch. C 16. The length of a rectangle is times a number. The width of the rectangle is 3 less than the square of another number. The length of the rectangle is greater than its width. a) Sketch a graph to represent this situation. Let the length of the rectangle be represented b units, and the width b ( 3) units. The length is greater than the width so an inequalit is: > 3, or >.5.75 The graph of the related function is congruent to.5 and its verte is (,.75). The curve is broken. Since cannot be negative, onl the region above the -ais is shaded. Also, 3>, so > 3 or < 3 Shade the region that satisfies these inequalities: >.5.75, >, > 3 Graph of.5.75, 3, 3 1 DO NOT COPY. P

7 b) Use the graph to list three possible sets of dimensions for the rectangle. Three sets of coordinates are: (, 1), (, ), (3, 3) So, three possible sets of dimensions are: width: ( ) 3 1; length: (1) width: 3 1; length: () width: 3 3 6; length: (3) 1 Possible dimensions are: 1 unit b units; 1 unit b units, 6 units b 1 units 17. Write a quadratic inequalit in variables that has these 3 points as solutions: A(, -3), B(-3, ), and C(3, 3) Sample response: Visualize the points on a grid. The highest point is (3, 3). Visualize a parabola that lies above the points; for eample, the parabola opens up, has verte (, ), and is congruent to. Its equation is: ( ) So, an inequalit is: <( ) 3

Lesson 5.2 Exercises, pages

Lesson 5.2 Exercises, pages Lesson 5. Eercises, pages 6 68 A. Determine whether each point is a solution of the given inequalit. a) - -16 A(-, ) In the inequalit, substitute:, L.S.: ( ) () 17 R.S. 16 Since the L.S.