17. f(x) = x 2 + 5x f(x) = x 2 + x f(x) = x 2 + 3x f(x) = x 2 + 3x f(x) = x 2 16x f(x) = x 2 + 4x 96
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1 Section.3 Zeros of the Quadratic Eercises In Eercises 1-8, factor the given quadratic polnomial In Eercises 9-16, find the zeros of the given quadratic function. 9. f() = f() = f() = f() = f() = f() = f() = f() = In Eercises 17-22, perform each of the following tasks for the quadratic functions. i. Load the function into Y1 of the Y= of our graphing calculator. Adjust the window parameters so that the verte is visible in the viewing window. ii. Set up a coordinate sstem on our homework paper. Label and scale each ais with min, ma, min, and ma. Make a reasonable cop of the image in the viewing window of our calculator on this coordinate sstem and label it with its equation. iii. Use the zero utilit on our graphing calculator to find the zeros of the function. Use these results to plot the -intercepts on our coordinate sstem and label them with their coordinates. iv. Use a strictl algebraic technique (no calculator) to find the zeros of the given quadratic function. Show our work net to our coordinate sstem. Be stubborn! Work the problem until our algebraic and graphicall zeros are a reasonable match. 17. f() = f() = f() = f() = f() = f() = Coprighted material. See:
2 474 Chapter Quadratic Functions In Eercises 23-30, perform each of the following tasks for the given quadratic function. i. Set up a coordinate sstem on graph paper. Label and scale each ais. Remember to draw all lines with a ruler. ii. Use the technique of completing the square to place the quadratic function in verte form. Plot the verte on our coordinate sstem and label it with its coordinates. Draw the ais of smmetr on our coordinate sstem and label it with its equation. iii. Use a strictl algebraic technique (no calculators) to find the -intercepts of the graph of the given quadratic function. Plot them on our coordinate sstem and label them with their coordinates. iv. Find the -intercept of the graph of the quadratic function. Plot the - intercept on our coordinate sstem and its mirror image across the ais of smmetr, then label these points with their coordinates. v. Using all the information plotted, draw the graph of the quadratic function and label it with the verte form of its equation. Use interval notation to describe the domain and range of the quadratic function. 23. f() = f() = f() = f() = f() = In Eercises 31-38, factor the given quadratic polnomial In Eercises 39-46, find the zeros of the given quadratic functions. 39. f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() =
3 Section.3 Zeros of the Quadratic 47 In Eercises 47-2, perform each of the following tasks for the given quadratic functions. i. Load the function into Y1 of the Y= of our graphing calculator. Adjust the window parameters so that the verte is visible in the viewing window. ii. Set up a coordinate sstem on our homework paper. Label and scale each ais with min, ma, min, and ma. Make a reasonable cop of the image in the viewing window of our calculator on this coordinate sstem and label it with its equation. iii. Use the zero utilit on our graphing calculator to find the zeros of the function. Use these results to plot the -intercepts on our coordinate sstem and label them with their coordinates. iv. Use a strictl algebraic technique (no calculator) to find the zeros of the given quadratic function. Show our work net to our coordinate sstem. Be stubborn! Work the problem until our algebraic and graphicall zeros are a reasonable match. 47. f() = f() = f() = f() = f() = f() = In Eercises 3-60, perform each of the following tasks for the given quadratic functions. i. Set up a coordinate sstem on graph paper. Label and scale each ais. Remember to draw all lines with a ruler. ii. Use the technique of completing the square to place the quadratic function in verte form. Plot the verte on our coordinate sstem and label it with its coordinates. Draw the ais of smmetr on our coordinate sstem and label it with its equation. iii. Use a strictl algebraic method (no calculators) to find the -intercepts of the graph of the quadratic function. Plot them on our coordinate sstem and label them with their coordinates. iv. Find the -intercept of the graph of the quadratic function. Plot the - intercept on our coordinate sstem and its mirror image across the ais of smmetr, then label these points with their coordinates. v. Using all the information plotted, draw the graph of the quadratic function and label it with the verte form of its equation. Use interval notation to describe the domain and range of the quadratic function. 3. f() = f() = f() = f() = f() = f() = f() = f() = 2 2 0
4 476 Chapter Quadratic Functions In Eercises 61-66, Use the graph of f() = a 2 + b + c shown to find all solutions of the equation f() = 0. (Note: Ever solution is an integer.)
5 Section.3 Zeros of the Quadratic Answers 1. ( + 2)( + 7) ( + 9)( + 1). ( )( + 1) ( 4)( 3) 9. Zeros: = 3, = ( 3,0) (6,0) 11. Zeros: = 13, = Zeros: = 4, = 1. Zeros: = 12, = 3 30 f()= f()= f()= ( 7,0) (2,0) ( 2,0) (18,0)
6 478 Chapter Quadratic Functions 23. Domain = (, ), Range = [ 9, ) f()=(+1) 2 9 = Domain = (, ), Range = (, 9] 20 ( 1,9) ( 2,8) (0,8) ( 4,0) (2,0) ( 4,0) (2,0) ( 2, 8) ( 1, 9) (0, 8) = 1 f()= (+1) Domain = (, ), Range = [ 16, ) 29. Domain = (, ), Range = (, 64] 20 f()=(+2) 2 16 = 2 ( 4,64) ( 8,48) 0 (0,48) ( 6,0) (2,0) ( 12,0) (4,0) 20 ( 4, 12) ( 2, 16) (0, 12) = 4 f()= (+4) (7 + 2)(6 1) 33. ( 3)( 4) 3. (4 )( + 1) 37. (2 + 7)( ) 39. Zeros: = /2, = Zeros: = 7/2, = Zeros: = 2/3, = 6
7 Section.3 Zeros of the Quadratic Zeros: = 3/2, = / f()= f()= (,0) (3.,0) ( 0.,0) (6.,0) Domain = (, ), Range = [ 32, ) =2 f()=2( 2) 2 32 ( 3,0) (.,0) ( 2,0) (6,0) (0, 24) (4, 24) (2, 32) 0 f()= Domain = (, ), Range = (, 18] ( 1,18) 20 ( 2,16) (0,16) ( 4,0) (2,0) = 1 f()= 2(+1) 2 +18
8 480 Chapter Quadratic Functions 7. Domain = (, ), Range = [ 7, ) 0 f()=3(+3) , , , 0 ( 8,0) (2,0) 20 ( 6, 48) (0, 48) ( 3, 7) = 3 9. Domain = (, ), Range = [ 121/2, ) 0 f()=2(+/2) 2 121/2 = /2 ( 8,0) (3,0) 20 (, 48) ( /2, 121/2) (0, 48)
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