REVIEW, pages

Transcription

1 REVIEW, pages a) Use a table of values to graph = b) Determine: i) the intercepts ii) the coordinates of the verte iii) the equation of the ais of smmetr iv) the domain of the function v) the range of the function Give the values to the nearest tenth where necessar. i) -intercepts: 4, 1 -intercept: 8 ii) From the graph, the ais of smmetr is midwa between 1 and. So, the equation of the ais of smmetr is 1.5. When 1.5, ( 1.5) 6( 1.5) 8, or 1.5 The coordinates of the verte are: ( 1.5, 1.5) iii) ais of smmetr: 1.5 iv) domain: ç v) range:» 1.5, ç 16. Which of these tables of values represents a quadratic function? Justif our response. a) b) The -coordinates increase The -coordinates increase b 1 each time. b 1 each time. First differences: First differences: ( 3) ( 13) The first differences decrease b The first differences are 4 each time. So, the function is constant. So, the function quadratic. is linear. 4 Chapter 4: Analzing Quadratic Functions Review Solutions DO NOT COPY. P

2 4. 3. Use graphing technolog to approimate the solution of the equation below. Write the roots to 3 decimal places = 0 Graph Use the CALC feature to displa X and X The roots are approimatel and For each pair of quadratic functions, describe how their graphs are related. a) = ( - 3) ; = ( + ) Compare the equations with ( p). ( 3) : Its graph is the graph of translated 3 units to the right. ( ) : Its graph is the graph of translated units to the left. So, the graph of ( 3) is translated 5 units left to get the graph of ( ). b) = + 5; = - 1 Compare the equations with q. 5: Its graph is the graph of translated 5 units up. 1: Its graph is the graph of translated 1 unit down. So, the graph of 5 is translated 6 units down to get the graph of 1. c) =- 1 ; = 1 Compare the equations with a. 1 Its graph is the graph of compressed b a : 1 vertical factor of, then reflected in the -ais. 1 : Its graph is the graph of compressed b a vertical 1 factor of. So, the graph of 1 is reflected in the -ais to get the graph of 1. P DO NOT COPY. Chapter 4: Analzing Quadratic Functions Review Solutions 43

3 For this quadratic function: = 1 ( - 4) - a) Identif the coordinates of the verte, the domain, the range, the direction of opening, the equation of the ais of smmetr, and the intercepts. a is positive, so the graph opens up. p 4 and q, so the coordinates of the verte are: (4, ) The equation of the ais of smmetr is p; that is, 4. To determine the -intercept, substitute 0: 1 (0 4) 6 The -intercept is 6. To determine the -intercepts, substitute 0: 0 1 ( 4) ( 6)( ) 6 or The -intercepts are and 6. The domain is: ç The graph opens up, so the verte is a minimum point with -coordinate. The range is:», ç b) Sketch a graph. The graph is congruent to the graph of 1. On a grid, mark a point at the verte (4, ). Use the step pattern. 1 Multipl each vertical step b ( 4) Chapter 4: Analzing Quadratic Functions Review Solutions DO NOT COPY. P

4 6. Determine an equation of the quadratic function for each set of data given. a) The coordinates of the verte are V(4, 1) and the graph passes through A(7, 6). An equation has the form a( p) q. The verte is at V(4, 1), so p 4 and q 1. The equation becomes a( 4) 1. Substitute the given coordinates for point A: 7, 6 6 a(7 4) 1 6 9a 1 6 9a a 3 So, the equation of the function is: 3 ( 4) 1 b) The graph passes through B(, -5) and has -intercepts -3 and 4. Use a( 1 )( ) Substitute: 1 3 and 4 a( 3)( 4) Substitute for B(, 5). 5 a( 3)( 4) 5 10a a 0.5 In factored form, the equation is: 0.5( 3)( 4) P DO NOT COPY. Chapter 4: Analzing Quadratic Functions Review Solutions 45

5 Write this equation in standard form. = ( 8) 45 Add and subtract: a 8 b 16 3( 8) 45 3( ) 45 3( 8 16) ( 4) Determine the intercepts, the equation of the ais of smmetr, and the coordinates of the verte of the graph of each quadratic function, then sketch the graph. a) = b) = The -intercept is 4. Factor the equation. 4 ( 1) ( 4)( 3) The -intercepts are: 4 and 3 The mean of the intercepts is: So, the equation of the ais of smmetr is: 0.5 Substitute 0.5 in 4 ( 0.5) ( 0.5) The coordinates of the verte are: ( 0.5, 4.5) The -intercept is 4. Factor the equation ( 8) 1 ( 4)( ) The -intercepts are: 4 and The mean of the intercepts is: 4 1 So, the equation of the ais of smmetr is: 1 Substitute 1in ( 1) The coordinates of the verte are: ( 1, 4.5) Chapter 4: Analzing Quadratic Functions Review Solutions DO NOT COPY. P

6 Select Audio Compan sells an MP3 plaer for $75. At that price, the compan sells approimatel 1000 plaers per week. The compan predicts that for ever $5 increase in price, it will sell 50 fewer MP3 plaers. Which price for an MP3 plaer will maimize the revenue? Let represent the number of $5 increases in the price of an MP3 plaer. When the cost is $75, 1000 are sold for a revenue of: $75(1000) $ When the cost is $(75 5), ( ) are sold for a revenue of $(75 5)( ). Let the revenue be R dollars. An equation is: R (75 5)( ) Use a graphing calculator to graph the equation. From the graph, the maimum revenue is about $ when the number of $5 increases is.5. The number of increases is a whole number, so round.5 to or to 3. Two increases of $5 mean that the MP3 plaer will now cost: ($5) $75 $85 Three increases of $5 mean that the MP3 plaer will now cost: 3($5) $75 $90 To maimize the revenue, the MP3 plaer should sell for $85 or $90. P DO NOT COPY. Chapter 4: Analzing Quadratic Functions Review Solutions 47