. ( 7, ) 9. (, 9 ) 0. (, 7). no solution. (, 7). no solution. no solution. ( 7, ). infinitel man solutions 7. (, 7 ). infinitel man solutions 9. (, 9) 70. 9a + a + 7. b b + 9 7. c + 90c + 7. 9d d + 7. m m + 7. n + n + 7. 77. q q + 7. -intercept:, -intercept: 79. -intercept:, -intercept: 0. -intercept: 7, -intercept: 7. -intercept:, -intercept:. -intercept:, -intercept:. -intercept: 9, -intercept: p 0 p +. +.. + 7.. 9. 90. 9. 7 + 9. g( ) + 9. g( ) + 9. g( ) + 9. g( ) + 9. infinitel man solutions 97. (,, 7 ) 9. infinitel man solutions 99. no solution 00. (,, ) 0. (,, 7) 0. in. b in. 0. a. You need 7. pounds of peanuts,. pounds of raisins,. pounds of pretzels, and pounds of chocolate cand pieces. b. Recipe B c. lbs 0. our friend; $.0 Chapter. Start Thinking Sample answer: f ( ) 0 f( ) 0 f( ) ( ) 0 f( ) 9 0 f ( ) f 0 f( ) 0 ( ) + 0 f( ) + The function f( ) ( ) is a horizontal translation unit right ( h ). The function f ( ) ( ) is a vertical stretch b a factor of ( a ). The function f( ) + is a vertical translation unit up ( k ). Copright Big Ideas Learning, LLC Algebra A9
. Warm Up. +. 0 + +. 0. a + a. The graph of g is a translation units right of the f(). 0. + +. Cumulative Review Warm Up. g ( ) +. g ( ). g ( ). Practice A. The graph of g is a translation units down of the g() ( ). The graph of g is a translation units left and unit down of the f() f() g() ( + ) g(). The graph of g is a translation unit up of the g() + f(). The graph of g is a translation unit left of the g() ( + ) 7. The graph of g is a reflection in the -ais followed b a vertical stretch b a factor of of the graph of f. f(). The graph of g is a reflection in the -ais followed b a horizontal shrink of the graph of f b a factor of. g() ( ) g() f(). The graph of g is a translation units right of the f() f() 9. The graph of g is a vertical shrink b a factor of of the f() g() g() ( ) A0 Algebra Copright Big Ideas Learning, LLC
0. When 0 < a < in the function g( ) a f( ), the transformation is a vertical shrink, not stretch; The graph of g is a reflection in the -ais followed b a vertical shrink b a factor of of the graph of the parent quadratic function.. The graph is a vertical stretch b a factor of, followed b a translation units left and units up of the parent quadratic function; (, ). The graph is a reflection in the -ais, followed b a vertical stretch b a factor of and a translation unit down of the parent quadratic function; (0, ). g ( ) ; (0, ). The graph of g is a translation unit right and units up of the g() ( ) +. The graph of g is a translation units right and units up of the f(). g ( ) 7; (0, 7) g() ( ) +. a. b. a h k g,, ; ( ) ( ) a h k g. Practice B,, ; ( ) ( ). The graph of g is a translation units up of the f(). The graph of g is a translation units left and units down of the g() + f() f(). The graph of g is a translation units left of the g() ( + ) 7. The graph of g is a reflection in the -ais, followed b a horizontal stretch b a factor of of the graph of f. f() f() ( ) g() g() ( + ). The graph of g is a translation units left and units down of the f(). The graph of g is a vertical shrink b a factor of, followed b a translation units up of the graph of f. g() + g() ( + ) f() Copright Big Ideas Learning, LLC Algebra A
9. The graph of g is a vertical shrink b a factor of, followed b a translation unit left of the graph of f. f() g() ( + ) 0. The graph is a reflection in the -ais, followed b a vertical stretch b a factor of and a translation units left and units down of the parent quadratic function; (, ). The graph is a vertical shrink b a factor of, followed b a translation units right and unit up of the parent quadratic function; (, ). Start Thinking 0 f( ) 0 V shape; es; es; The line of smmetr is the -ais.. Warm Up f(). P (, ). P (, ). P (, ). P (, ). Cumulative Review Warm Up. linear; ; 0; After jogging for 0 minutes, 0 calories were burned.. ( + ) g ( ) ; (, 0). g ( ) (+ ) ; (, ). h ( ) f( ) + Add to the output. + Substitute ( ). Enrichment and Etension + + + ; ( ) ; ( ) ; + ( ) ; ( ) ; + + + ( ) ; ( ) f and simplif. g( ) h( ) Multipl the input b. into h ( ) and simplif. + + Substitute. not linear. Practice A.. f() ( ) (, 0).. g() ( + ) + (, ) f() ( + ) (, 0) h() ( ) (, ). Puzzle Time EL SALVADOR. ( ) + (, ) A Algebra Copright Big Ideas Learning, LLC
.. f() ( + ) (, ) 0 f() (0, ) 7.. Both graphs have the same ais of smmetr,.. 9. + (, ) (, 0) + + (, 7) + +. C; It has the largest leading coefficient, a.. minimum: ; domain: all real numbers, range: ; increasing to the right of 0; decreasing to the left of 0. minimum: ; domain: all real numbers, range: ; increasing to the right of 0; decreasing to the left of 0 7. maimum: ; domain: all real numbers, range: ; increasing to the left of ; decreasing to the right of. maimum: ; domain: all real numbers, range: ; increasing to the left of ; decreasing to the right of 9. a. noon b. 7 customers. Practice B 0. (, ) f() +.. (, ) f() ( + ) + (, ) f() ( ). 0 g() + (0, ).. (, ) g() ( + ) + (, ) h() ( ) Copright Big Ideas Learning, LLC Algebra A
cm 7 in.. 0.( ) 7. maimum: ; domain: all real numbers, range: ; increasing to the left of ; decreasing to the right of. (, 0) f() 0.. minimum:.; domain: all real numbers, range:.; increasing to the right of ; decreasing to the left of 9. a. The maimum height occurs mile from the base of the bridge. 0 (0, ) b. The maimum height is mile. 7.. (0, ) 0 + 7 + (0, ) 0. Enrichment and Etension... +. +. + + +. + + 9. 0.. + f() 0. + 7. no; The definition of a quadratic function sas a 0, but for the ais of smmetr to be undefined, a would have to be 0... (, ) + (,.). lowest; The -values on either side of are greater than.. A; Both have an ais of smmetr of.. minimum: ; domain: all real numbers, range: ; increasing to the right of 0; decreasing to the left of 0. maimum: 9; domain: all real numbers, range: 9; increasing to the left of ; decreasing to the right of (,.) (, ) f(). Sample answer: (,0); The -value 7 is units awa from the verte -value. Because the -value is also units awa from, it has the same output value 0.. Puzzle Time THIS BRITISH ROWER WAS THE FIRST WOMAN TO ROW ACROSS THREE OCEANS.. Start Thinking Sample answer: D(, ) C(, ) cm 7 B(, ) P ( 0, in. ( A(, ) es; Point P is the same distance from the parabola as the line is to the parabola. So, it will alwas ield the same distance as long as the measurement is taken from a point on the graph of the parabola. A Algebra Copright Big Ideas Learning, LLC
. Warm Up..7.... 7...... Cumulative Review Warm Up. 0.7.. z 0. z... Practice A...... 7. A; The directri is below the focus.. focus: (0, ), directri:, ais of smmetr: 0. in.; The receiver is at the focus...... 7.. verte: (, ), focus: (, ), directri: 0, ais of smmetr: ; The graph is a vertical shrink b a factor of, followed b a translation unit right and units up. 9. verte: (, ), focus: (, ), directri: 0, ais of smmetr: ; The graph is a vertical shrink b a factor of, followed b a reflection in the -ais and a translation units left and units down. 0. verte: (, ), focus: (, ), directri:, ais of smmetr: ; The graph is a translation units right and units down.. verte: (, 0), focus: (, ), directri: 7, ais of smmetr: ; The graph is a vertical shrink b a factor of, followed b a reflection in 7 the -ais and a translation units left and 0 units up. 9. focus: (0, ), directri:, ais of smmetr: 0. Practice B... 0... 7. focus: (0, ), directri:, ais of smmetr: 0 0. focus: (, 0), directri:, ais of smmetr: 0 Copright Big Ideas Learning, LLC Algebra A
. focus: (, 0), directri:, ais of smmetr: 0.... 7.. 9. 0. 9. focus: (, 0), directri:, ais of smmetr: 0 0. focus: (0, 9), directri: 9, ais of smmetr: 0 0,, directri: ais of smmetr: 0. focus: ( ) 0,, directri:, ais of smmetr: 0. focus: ( ) 0 + 0,. verte: (, ), focus: ( 7, ), directri:, ais of smmetr: ; The graph is a shrink towards the -ais b a factor of, followed b a reflection in the -ais and a translation units left and units up.. verte: ( ) (, ), focus:,, directri:, ais of smmetr: ; The graph is a vertical stretch b a factor of, followed b a translation units left and unit down.. verte: 9 ( ) (, ), focus:,, directri:, 0 0 ais of smmetr: ; The graph is a stretch awa from the -ais b a factor of 0, followed b a translation units right and units down.. verte: (, 9), focus: (, ), directri: 7, ais of smmetr: ; The graph is a vertical shrink b a factor of, followed b a reflection in the -ais and a translation unit left and 9 units up.. Enrichment and Etension.. a. b.. RS has a slope of n n s r ( s r)( s + r) s + r r + s. s r s r t 0 t OT has a slope of t. t 0 t Because RS and OT are parallel lines, their slopes are equal. So, r + s t. A Algebra Copright Big Ideas Learning, LLC
. To find the midpoint of a line segment, find the average of the -values and -values of the endpoints. The -value of the midpoint of RS would be r + s. t The -value of the midpoint OT would be. u + v The -value of the midpoint UV would be. UV has as slope of v u ( v u)( v + u) v + u u + v. v u v u Because UV is parallel to both RS and OT, all slopes are equal and u + v r + s t. So, the -values of their midpoints are all the same t r + s and lie on the same line, or or u + v.. Puzzle Time YELLOWSTONE PARK. Start Thinking Sample answer: 0.; After weeks, ou have $0. in our bank account.. Warm Up. ( ). ( ). + ( ). + ( ) + ( ). + ( ). Mone in bank account 0 0 Your Checking Account Weeks. Cumulative Review Warm Up.... The graph is a vertical stretch b a factor of, followed b a translation unit down of its parent function. The graph is a vertical stretch b a factor of, followed b a reflection in the -ais of its parent function. The graph is a vertical stretch b a factor of, followed b a translation 7 units up of its parent function. The graph is a reflection in the -ais, followed b a translation units right and unit down.. Practice A.. f() h() g() 0 f() 0 7 ( ). ( ) 9( + ) +. ( 0)( ). ( )( ). 7 ( + )( + ) 0 0 f() f() ( ) h() g() + 7 0 0 Copright Big Ideas Learning, LLC Algebra A7
7. a. b. 9 ( ) 0 0 9 9 9 + + + c. 9 ( + )( ) d. 0 0 9 9 9 + + e. es; intercept form; Two intercepts were given.. 9. ft. Practice B. ( ). + + 9. ( ) +. ( )( ). ( + 7)( + ). ( 9)( 9) + 9 9 ( ) 7. The two given sets of coordinates were not substituted into the correct places. 7 a ( h) a( ) + k 7 a a a The equation is ( ).. a. The maimum area of 00 square feet occurs when the length is 0 feet. b. A ( ) + 00 ; A() 9 ft c. 0 to 0 ft: ft 0 ; 0 to 00 ft: ft. Enrichment and Etension. linear;. +.0. quadratic a..9 + 9. +. b. +.9( ) 7. ft 0 ft c. The graph of the function is a reflection in the -ais, followed b a vertical stretch b a factor of.9 and a translation units right and 7. units up of its parent function.. quadratic a. + 0 + b. + ( ) 7 c. The graph of the function is a reflection in the -ais, followed b a vertical stretch b a factor of and a translation units right and 7 units up of its parent function.. linear; 0. +.7. quadratic a. + + b. + (.). c. The graph of the function is a reflection in the -ais, followed b a vertical stretch b a factor of and a translation. units right and. units up of its parent function.. Puzzle Time PINK FLAMINGO Cumulative Review..... 7. 7.. 9. 0. 9.... 7.. 7. a. 9% b. 9% c. correct answers d. 0 correct answers. a. 9% b. 7% c. correct answers d. correct answers e. correct answers 9. cups 0. tablespoons... 7.07... 0...7. 7.07 7..7. 7. 9. 0. A Algebra Copright Big Ideas Learning, LLC
0. 9.. 0.00. 0.00..0. 7.0..0. 9 7.. or 9 9. 0. 0 7 7...... 7. + 7. + 7 9. + 0.. + 0.... no solution. no solution 7. no solution. 9 7. ( )( + 7). ( + )( + ) 9. ( + )( ) 90. ( )( + ) 9. ( + )( ) 9. ( )( ) 9. ( + )( + ) 9. ( )( ) 9. ( + )( + ) 9. ( + 7)( ) 97. ( + 0)( ) 9. ( )( + 0) 99. ( )( 0) 00. ( )( + ) 0. ( )( + ) 0. ( )( + ) 0. ( + 9)( 9) 0. ( + 0)( ) or ( )( + ) 0. 0. 07. + + + 9. 0. 00.. 00.. 9. no solution. h 7.. h. about. h 9. 70. 7. + 7 9 7. 7. 0 + 0 7. + 7 7. 7 7 + 9 7. 77. + 7 7. 0. 09. 0....... 7.. + + 7 + 0 9 + 7 7 + + 7 + 0 + + 7 + + 7 7 70 7 79. 0. + 9. + 9 7. +. 7 7 7 0.. +. ( + )( ). ( + )( 7). ( )( + ).. + 0 + + Copright Big Ideas Learning, LLC Algebra A9
. in.. ft. in... in. 7. ± i f(). ± 9. ± 7 h() The graph of h ( ) is a vertical shrink b a factor 0. ± i 7 of and a reflection in the -ais of the graph of f ( ).. ± 0. ± 9... 7 ± 9. 7 ± 9. ± i 7 ± i 9 f() c() 7. 7 ± i 7. ± i 7 The graph of c ( ) is a vertical translation units down of the graph of f ( ). 9. ± i 0. ± i 9 0.. ± i. ± i d() f(). ±. ± i The graph of d( ) is a vertical stretch b a factor of of the graph of f ( ).. 9 ± 0. ± i. 7. f() f() k() + g() The graph of g( ) is a vertical stretch b a factor of of the graph of f ( ). The graph of k ( ) is a horizontal translation units left of the graph of f ( ).. The graph of m ( ) is a translation units right and units up of the graph of f ( ). m() + f() A0 Algebra Copright Big Ideas Learning, LLC
. g ( ). g ( ) 7 +. g( ) + +. g ( ) 7 7. g( ). g( ) + + 9. g ( ) 0. g ( ) +. no solution.,. (, ) or about ( 0.7,.9). Cumulative Review Warm Up. f() ( + ) Chapter. Start Thinking (, 0). g() ( ) (, ) Equation Number of -intercepts Point(s) ( 0, 0 ) ( 0, 0 ) (, 0 ), (, 0) 0 N/A.. (, ) ( + ) f() + (0, ) Yes, there are patterns; Sample answer: A quadratic equation has one -intercept when the verte is on the -ais. If the quadratic equation opens down, the graph has two -intercepts if the constant is positive and none if the constant is negative. If the quadratic equation opens up, the graph has two -intercepts if the constant is negative and none if the constant is positive; The verte is a minimum if the term is positive; The verte is a maimum if the term is negative.. Warm Up. (, ). (, ). infinitel man solutions. Practice A 0. and.. and. and. and. and Copright Big Ideas Learning, LLC Algebra A