find the constant of variation. Direct variations are proportions.

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1 Algera 1 Quadratics, Inverse Variation, COBF Test Study Guide SOLs A.4 A.7 A.8 A.11 Name Date Block Algera 1 Quadratics, Inverse Variation, Curve of Best Fit Test STUDY GUIDE The standard form of a paraolic quadratic function is f() = a c We can sketch a quadratic of the form a c y finding: o Its concavity: concave up (positive a) or concave down (negative a) o The y-intercept (occurs at f(0), and is the same value as c) o The ais of symmetry, the vertical line that divides the paraola into two symmetric parts; the ais of symmetry is = o The verte: the verte always occurs on the ais of symmetry, so its -value is ; find the y-value of the verte y plugging into the equation. o The numer of zeros: use the discriminant 2 4ac: If 2 4ac is positive, there are two zeros If 2 4ac is zero, there is one and only one zero If 2 4ac is negative, there are no real zeros o The zeros (-intercepts), if any; find zeros using one of these methods: Graph using the graphing calculator; find the zeros y oservation (or use the zeros function to find the values of the zeros) Set the equation equal to 0 (all terms on one side; 0 on the other) Solve y factoring (factor; set each factor equal to 0 and solve) 2 4ac Solve y quadratic formula: = Solve y completing the square: half it, square it Determine if a function is a direct variation, inverse, variation, or neither: o Direct variation is linear and always has a y-intercept through the origin, and is of the form y = k, where k is the constant of variation. We can rewrite it as k = y to find the constant of variation. Direct variations are proportions. o Inverse variation graphs as hyperolas, and is of the form y = k, where k is the constant of variation. We can rewrite it as k = y to find the constant of variation o Use these facts to determine if a tale of values is a direct variation, inverse variation, or neither. o Solve word prolems ased on whether two variales vary directly or inversely. Model data using a quadratic regression o Use the calculator to find the quadratic curve of est fit for data, and make predictions ased on this data o Use the coefficient of determination (R 2 ) to determine if the curve of est fit is a etter model than the line of est fit. The closer R 2 is to 1, the etter.

2 Algera 1 Quadratics, Inverse Variation, COBF Test Study Guide Page 2 Study Questions 1) What are the zeros of the function shown at right? 2) Use the discriminant to find the numer of real solutions: a) = 0 ) = 0 c) = 8 3) Sketch the graph of the following quadratics, providing the information requested. a) f() = ) f() = zeros (if any): c) f() = d) f() = ) Find the c value that completes the square. Then write the product as a inomial squared. a) c ) c c) c d) c

3 Algera 1 Quadratics, Inverse Variation, COBF Test Study Guide Page 3 5) Solve y completing the square: a) = -5 ) = 0 c) = 0 d) = -8 6) Determine whether the following equations represent direct variation, inverse variation, or neither. a) y = 5 10 ) y = c) 3 2y = 10 d) y = 12 e) y = 5 7) Find the constant of variation. Then write the equation of the function. a) varies directly as y, and = 3 when y = 9 ) varies inversely as y, and = 4 when y = -8 k = c) varies directly as y, and (4, 16) is a point on the function. k = k = d) varies inversely as y, and (-3, 6) is a point on the function. k = 8) Determine whether the following tales represent a direct variation, inverse variation, or neither. If it is a direct variation, write the equation. If it is neither, leave the equation lank or write n/a. a) c) y y ) d) y y ) Jaco works a jo where the money he earns varies directly to the hours he works. In one week, Jaco worked for 15 hours and made $ How many hours did Jaco work in his second week if he earned $117? 10) A local fast food restaurant takes in $9,000 in a 4 hour period. How many hours would it take the restaurant to earn $20,500?

4 Algera 1 Quadratics, Inverse Variation, COBF Test Study Guide Page 4 11) The force F needed to loosen a olt with a wrench varies inversely with the length l of the handle. It takes 250 ls of force to loosen a olt with a 6 inch long handle. How much force is needed for a 24 inch long handle? 12) The volume, V, of a gas varies inversely as the pressure, p, in a container. If the volume of a gas is 200cc when the pressure is 1.6 liters per square centimeter, find the volume (to the nearest tenth) when the pressure is 2.8 liters per sq centimeter. 13) On Tuesday, May 10, 2005, 17 year-old Adi Alifuddin Hussin won the oys shot-putt gold medal for the fourth consecutive year. His winning throw was meters. A shot-putter throws a all at an inclination of 45 to the horizontal. The following data represent approimate heights for a all thrown y a shot-putter as it travels a distance of meters horizontally. a) Draw a scatter plot of the data. ) Use the calculator to find the linear regression equation (round coefficients to the nearest hundredth). Find r 2, the coefficient of determination. c) Use the calculator to find the quadratic regression equation (round coefficients to the nearest hundredth). Find R 2, the coefficient of determination. d) Compare the coefficient of determination (R 2 ) of the quadratic model with the same value (r 2 ) for the linear model. Which model is a etter fit for the data? Eplain how you came up with your conclusion. e) Use the quadratic model to predict the height of the all if it travels 80 meters. f) Use the quadratic model to predict the height of the all if it travels 100 meters. Eplain whether this prediction makes sense or not.

5 Algera 1 Quadratics, Inverse Variation, COBF Test Study Guide Page 5 STUDY QUESTION ANSWERS 1) = -3, 2 2) a) one solution ) no solutions c) two solutions 3) a) up; ais of sym: =3; verte: (3, - 1), y-int = 8; zeros = 2, 4 ) down; ais of sym: =-1; verte: (-1, 4), y-int=3; zeros =-3, -1 c) up; ais of sym: =-1; verte: (-1, - 1), y-int=3; zeros =-1/2, -3/2 d) up; ais of sym: =-2; verte: (-2, -4), y-int=8; zeros = -3.15, ) a) c = 9; ( 3) 2 ) c = 1; ( + 1) c) c = ; d) c = ; ) a) = -1, -5 ) = -1, 9 c) = 3± , 5.45 d) = 2± , ) a) direct ) inverse c) neither d) inverse e) direct 32 7) a) k = 3; y = 3 ) k = -32; y = -32 or y = - c) k = 4; y = 4 d) k = -18; y = or y= ) a) neither (no equation) ) inverse; y = c) direct; y = -9 d) inverse; y = - 9) 12 hours 10) 9.11 hours 11) 62.5 ls 12) cc 13) a) see right ) y= ; R 2 =.588 c) y = ; R 2 =.97 d) quadratic model is etter ecause R 2 is closer to 1 e) aout 14 m f) aout -4.8 m; no ecause height can t e negative