4. exponential decay; 20% 9.1 Practice A found square root instead of cube root 16 =

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1 9.. eponential deca; 0% 9. Practice A found square root instead of cube root 6 = = = 9. = 7, 9. =,.. 7n 7n. 96. =, 97. =, 9. linear function: = quadratic function: = eponential function: = Chapter 9 9. Start Thinking 60:,,,,, 6,, 9, 0,,,, 0,, 0, 6, 0,, 60, 7, 90, 0, 0, 60 Greatest perfect square: 6 60 = 6 0 = 6 0 = Warm Up Cumulative Review Warm Up. eponential deca; 0%. eponential growth; %. eponential deca; % w w Practice B. t t z n n q. p p d not full simplified; the denominator contains a radical = = k k t 6t A0 Algebra Copright Big Ideas Learning, LLC

2 7. h d d m = 6. g = org = 9. Practice A. =,. =,.. 9. Enrichment and Etension + +. i. i. 6i 6. iwz. ir 7pq 6. i 7. i. i 9. i 0 0. i 0. 9i. i.. = 0. + = 0 + = 0 6. = 0, 7. =. no solution 9. =, 0. no solution. =,. a. The indicate when the height is zero. b. ft. = 6,. =,. =, 0. i 0 9. Puzzle Time. i THANK YOU FERRY MUCH. i 6. f() = + 9. Start Thinking = 0.,.6 7. f() = + 6 The parabola crosses the -ais twice. The points are, 0, 0. ( ) and ( ) The zeros of the function show the same points because a zero is another name for a point where the parabola crosses the -ais. These points are called zeros because the represent the point(s) on the parabola where the - value is zero. 9. Warm Up. =. b =. =. 0 = 6 0., 7. = +. =. = 0 6. n = 9. Cumulative Review Warm Up. = 0or = 9. t = 0ort = = 7.6,.6. s = 0ors = 0. a = ora = Copright Big Ideas Learning, LLC Algebra A09

3 9.. = + = + no solution no solution 0. = ft Practice B. =. no solution.. = 0. + = = , = 7. = 6. no solution 9. =, 7 0. no solution. = 9,. a. no; Time cannot be negative. b. sec. = 7,. =,. =, 6. 6 = + = 0., ft 9. Enrichment and Etension. a.. sec and sec b. 6. sec. 60 ft.. ears; in 99. a. 000 tires b. $ 9. Puzzle Time IT HAS NO STEPS f() = + + =.6, f() = + =, A0 Algebra Copright Big Ideas Learning, LLC

4 9. Start Thinking Replacing f ( ) with zero and moving the constant ields the following equations: = = 9 = = 0 0 = = 9 When the constant is positive, there are two solutions; when the constant is zero, there is one solution; and when the constant is negative, there are no solutions. 9. Warm Up. =. = 6. w =. a = 9. Cumulative Review Warm Up. even. neither. neither. odd 9. Practice A. two; = 6, 6. zero. one; = 0. =,. no solution 6. no solution 7. =,. = 6, 6 9. = 0 0. =. =,. Function ( ) f Number of zeroes = ( ) f = 9 ( ) f = ( ) f = ( ) f = + 0 ( ) f = =,. =±.. =±.. =±. 6. The square root does not distribute over subtraction, so 9 does not equal. Begin b isolating on the left side. 7. a. 9 = 6 = = ± w = 6 b. width cm, length cm. At =±, because 9. At =±., because 9. Practice B =. =... two; =,. zero. two; =,. no solution. =, 6. = 0 7. =,.. =, 9. =,. 9 9 =, 0. =, =,. =±.6. =±.. =±. 6. The right side becomes negative after subtracting, so the equation does not have a real solution. + = 9 = 6 no solution 7. a. 0πr = 60π b. in.. a. =, b. =, c. =, 9. Enrichment and Etension. = 0; multiplicit of ; rational. =± i; imaginar. = ± i ; imaginar Copright Big Ideas Learning, LLC Algebra A

5 . = ± ; irrational =± ; irrational i = ± ; imaginar 7. =± ; i imaginar. i 0 = ± ; imaginar 9. = ± i; imaginar 9. Puzzle Time HOW ABOUT SECONDS 9. Start Thinking (, ) The minimum and the verte are the same point for the function. A quadratic function has a minimum when the parabola opens up and a maimum when the parabola opens down; these correspond to positive and negative leading coefficients, respectivel. 9. Warm Up (, ). ( + )( ). ( + ). ( + )( ). ( ). ( a + ) 6. ( + 7)( 7) 7. ( a + ). ( a ) 9. Cumulative Review Warm Up. z =. m =. c =. =. g = 6. h = 7. n = 0. n = 9 9. Practice A. c = 9. c =. c = + =. ( ) = 0. ( ) = + 6. ( ) 7. = 0.69,.69. =, 9. =., a. w + w = 60 b. width ft, length 0 ft. no solution. =,. =., 6.. =, 7. =.6,.6 6. = 0.,. 7. Divide ever term b.. minimum of 9. minimum of 6 0. maimum of 9. minimum of 0. a. + = b. and 6 9. Practice B. c = = 7 c =.. ( ) = +. ( ) = c = 7. =.,.. =.,. 9. =.76, a. = 0 b. width 6 ft, length ft 9 A Algebra Copright Big Ideas Learning, LLC

6 . =.7, 7.. = 0.,.. no solution. = 9.7, 0.. = ( ), V(, ). =.6,.6 6. =.7,.7 7. b = ±. minimum at 9. minimum at 9 0. maimum at. minimum at. a. + = b. 7 and 9 9. Enrichment and Etension. = ( ) + ; V(,) 9. = ( ) + ; V(,) 6. = ( + ) ; V(, ). = ( + ) ; V(, ) 7. = ( + ) ; V(, ) 6. = ( + ) ; V(, ). = ( ) + ; V(,) 6 Copright Big Ideas Learning, LLC Algebra A

7 9. = ( + ) 6; V(, 6). 7 < < no solution 9. Practice A 6. + = 0; a =, b =, c = = 0; a =, b =, c = 0 9. Puzzle Time A HARE RESTORER 9. Start Thinking When a = 0, the Quadratic Formula is undefined because ou cannot divide b zero. In this case, the function has no term, and is therefore not quadratic but linear. The other situation that makes the Quadratic Formula undefined is when b ac < 0. Note: In this case, the equation is technicall still solvable, using the set of imaginar numbers. 9. Warm Up Cumulative Review Warm Up. w orw 7. < u <. < f < v or v = 0;, a = b = 7, c =. =. no real solution 6. =, no real solution =, = =,. = 0.,.. a. 0. and 0. sec b.. sec. one. two. zero 6. two 7. zero. two 9. = ± ; Using Square Roots; in the form 0. no real solutions; Quadratic Formula; doesn t fit the other methods. = 0.,.; completing the square; a = and b is even.. =.,.; Quadratic Formula; doesn t fit the other methods. = 7; factoring; Perfect Square Trinomial. = 0, ; factoring; eas to factor. a. 7 < 0; no real solutions b. + 6 = 0 c. no; Both equations have zero solutions; the sign of b does not affect the discriminant because b is squared. 9. Practice B. + 9 = 0; a =, b =, c = 9 = d A Algebra Copright Big Ideas Learning, LLC

8 = 0; 7, 0 7 0; a = b = 6, c = = a =, b = 0, c = 7. =. =, 9.6 Start Thinking = 6. =, 7. = 0., 0.. no real solution 9. = 0. = 0.,.. no real solution. a. 6. and. sec b.. sec Sstem has two solutions because the graphs of the equations intersect at two points. = -0. zero. two. one 6. one 7. zero. two 9. = 0.6, 0.6; completing the square; a = and b is even. 0. = 0, ; factoring; eas to factor. no real solution; using square roots; in the form = d. = 0.,.; Quadratic Formula; doesn t fit the other methods. =.,.9; Quadratic Formula; doesn t fit the other methods. = 6; factoring; Perfect Square Trinomial. a. 7 < 0 b. + 6 = 0 c. es; The original equation has zero solutions and the new equation has two solutions; changing the sign of c changes the discriminant from negative ( ) to positive ( ) 9. Enrichment and Etension. 9 in. Sstem has one solution because the graphs of the equations intersect at one point. Sstem has no solution because the graphs of the equations do not intersect. 9.6 Warm Up. (, ). (, ). (, ). (, ) 9.6 Cumulative Review Warm Up. = + = =6+ 6 = length: 9 km, width: km 6. width: in., height: 6 in.. base:.7 in., height:. in.. height: 0. cm, base: cm 9. Puzzle Time THEIR TRUNKS -intercept: (, 0 ) Copright Big Ideas Learning, LLC Algebra A

9 .. a zero between and ; a zero between and 0. a zero between and ; a zero between and. at t =.7 sec. -intercept: ( 0, 0 ) 9.6 Practice B. (, ), (, ). (, 0 ), ( 0, ). (, ). no real solution. (, ) 6. no real solution 7. ( 7, ), (, ). ( 0, ) 9. (, ) 0. (, ), (, ). (, ), (, 7). (, ), (, 0). a zero between 0 and. a zero between 0 and ; a zero between and -intercept: (, 0). Sample answer: ( ) f =.6 +.6;. g( )..; solutions are (.,.6 ), ( 0.7,.9 ). = corresponding 9.6 Enrichment and Etension. a. at t = sec, and then again at t = sec b..09 sec. 0, or 0 jackets. items -intercept:,0 9.6 Practice A. (, ), ( 0, ). no real solution. (, ). (, ), (, ). ( 0, ), (, 0) 6. (, ) 7. ( 7, ), (, ). (, ), (, ) 9. (, ), (,) 0. (, ), (, 0). no real solution. (, ), (, 0). a. es b. about 0. and 0.6 sec. a. about 0.9 sec b..07 sec 9.6 Puzzle Time TO BE ABOVE IT ALL Cumulative Review. =. =, =. h 0 A6 Algebra Copright Big Ideas Learning, LLC

10 .. no solution 6. a b. at least h = 9. = 0. g =, 6 9. g = 0, 0. ( m )( m ). ( z + )( z 7). ( w )( w ) + +. sec. z =, z =. = 6. ( )( ) 7. ( 7)( ) vertical stretch b a factor of 0. vertical shrink b a factor of 0.7. = +. = 0.. = 6. (, ). ( 6, ) 6. no solution 7. $7 for a small bo and $ for a large bo. 9 z 9. 7m vertical shrink b a factor of and a reflection in 7 the -ais 0. z. = Copright Big Ideas Learning, LLC Algebra A7

11 .. 6 translation 6 units up. 6 domain: all real numbers; range: 9. maimum: 0. minimum: 9. verte: (, 0 ); ais of smmetr: =. verte: (, 0 ); ais of smmetr: =. verte: (, ); ais of smmetr: = vertical stretch b a factor of, followed b a translation 7 units up.. translation 6 units to the left and a vertical stretch b a factor of 7 vertical shrink b a factor of, and a reflection in the -ais, followed b a translation units down.. a. sec b. If k is positive, it will increase part (a); if k is negative, it will decrease part (a).. a. ais of smmetr : = b. verte: (, 0) 6. a. ais of smmetr: = 7. b. verte: (, 0) translation units to the right and units down, followed b a vertical shrink b a factor of domain : all real numbers; range: A Algebra Copright Big Ideas Learning, LLC

12 no solution 9. in. b in. Chapter 0 0. Start Thinking. quadratic function; = The domain of the function is all positive real numbers and zero. The range is also all positive real numbers and zero. You cannot use negative numbers in the domain because the square root function cannot be evaluated using negative numbers in this course = 9, = 66. =, = 67. =, = 6. =, = 69. =± 70. =± 7. no real solutions 7. sec The calculator is able to graph this function because negative numbers and zero will allow the radical to be evaluated. This function has an inverse domain when compared to =. 7. =, = 7. =, = 0 7. w 7., w. 76. t = 7, t = 77. n =, n = 7. h 79. a square fence, with side length ft 0. =, =. =, h = =, = 0. Warm Up.. w = 0., w =.9. z =., z =.. 0 -intercepts. -intercept. 6. -intercepts intercepts. (, ) and (, 0) 9. (, ) and (, ) Copright Big Ideas Learning, LLC Algebra A9