TEST REVIEW QUADRATICS EQUATIONS Name: 2. Which of the following statements is true about the graph of the function?

Transcription

1 Chapter MATHEMATICS 00 TEST REVIEW QUADRATICS EQUATIONS Name:. Which equation does not represent a quadratic function?. Which of the following statements is true about the graph of the function? it has two -intercepts it opens downward The ais of smmetr is = the verte is at the origin. What are the coordinates of the verte for the quadratic function (7,) (7,) (-7,) (-7,). What is the ais of smmetr for the quadratic function = -8 = 8 = 9 = -9. Which function has a maimum value of? ( ) 6. What characteristics describe the graph of? verte at (0, ), opens down verte at (0, ), opens up verte at (0,), opens down verte at (0,), opens up 7. Which graph represents the function? Which function best represents the given graph?

2 9. Which of the following statements is true about the graph of the quadratic function shown? A) The equation of the ais of smmetr could be = 0. B) The range could be { <, R}. C) The verte could be (, ). D) The -intercept could have a value of. 0. Suppose that the graph of the function f () = is reflected in the -ais, translated units to the left, and then translated units upward. Which could be the resultant function? f () = ( + ) + f () = ( ) + f () = ( ) + f () = ( + ) +. The graph of has been transformed as shown. What is the value of the parameter a?. What is the range of? {, R} {, R} {, R} {, R} Which function has a domain and range? ( ) ( ). What is the range of the quadratic function ( )?, R, R, R, R. What is the -intercept of? Which quadratic function has verte (, 0) and passes through (6, -)? 7. For what value of does the function have a maimum value?

3 8. What is the standard form of ( )? What is the Standard Form of the function? Which function describes the graph provided? Which describes the -coordinate of the verte of? 9 6, minimum value, minimum value 9 6, maimum value, maimum value. What is the verte form of 6? 7. What is the verte of the graph of the function 8? (,0) (,9) (,0) (,9). What is the equation of the ais of smmetr for? 7. Which is the ais of smmetr for the graph of the function? 6. What is the Verte Form of? 8 ( ) ( ) ( 8) 7 ( 8) 7 7. A football follows a path defined b h( t) t 6t where h is height in metres and t is time in seconds. At what time, in seconds, does the football reach its maimum height? 6 9

4 8. The path of a model rocket is modeled b the function h(t) = -.9t + 96t, where h(t) is height in metres and t is elapsed time in seconds. What is the maimum height in metres reached b the rocket? A quadratic function is given b ais of smmetr is? b. What is the value of b if the equation of the The path of a volleball is given b, where t is time in seconds and h is height in meters. At what time, in seconds, does the ball reach its maimum height? 0... The school cafeteria sells 0 bottles of juice at a cost of $. If for ever 0 cent decrease in cost there is an increase in sales of bottles, which equation describes the revenue? R ( 0 )( 0.0) R ( 0 0)( ) R ( 0 0)( ) R ( 0 )( 0.0) CONSTRUCTED RESPONSE REVIEW:. Sketch the graph of A) Identif Ais of Smmetr Verte Direction of opening Maimum or minimum situation [circle one] (E) Maimum or minimum value (F) Y-intercept (G) Number of -intercepts (H) Domain: (I) Range: B) Identif Ais of Smmetr Verte Direction of opening Maimum or minimum situation [circle one] (E) Maimum or minimum value (F) Y-intercept (G) Number of -intercepts (H) Domain: (I) Range:

5 . Determine a quadratic function in verte form that has the given characteristics. a) its verte at (, 0) and passes through the point (, ) b) its verte at (, ) and passes through the point (, ) c) its verte at (, ) and has an -intercept of (, 0) d) its verte at (, ) and has a -intercept of (0, ). Determine a quadratic function in verte form for each parabola. a) b). Rewrite each quadratic function in verte form. a) = 6. b) = 8 6. A ball is kicked from an initial height of m and follows a parabolic path as shown. After seconds the ball reaches a maimum height of m. Determine the quadratic function that models the path followed b the ball. Use the quadratic function to determine the height of the ball at seconds. m 7. A soccer plaer kicks a ball from the ground towards a wall that is 8 m awa. The ball reaches a maimum height of 9 m when it is a horizontal distance of m awa from the plaer. Determine the quadratic function that models this situation. Determine the domain and range At what height from the floor will the ball hit the wall? 8. A total of 0 m of fencing is used to make a divided rectangular region as shown. Algebraicall determine the maimum area that could be enclosed. 9. An airline compan transports 00 passengers each da between two cities for a one wa fare of $60. Research indicates that for each fare increase of $, the number of passengers will decrease b 0. Determine the ticket price that will result in the greatest revenue for the airline. 0. A rectangular region, placed against the wall of a house, is divided into three regions of equal area using a total of 0m of fencing as shown. Algebraicall determine the function which gives the area of the entire region as a function of its width, and use this function to calculate the maimum possible area.

6 6. A theatre seats 00 people per show and is currentl sold out with a ticket price of $0. A surve shows that for ever $ per ticket price increase, fewer tickets will be sold. Write a function to model this situation and use this function to determine the ticket price that will result in the greatest revenue per show.. The sum of two numbers is and the sum of their squares is a minimum. Algebraicall determine the function that models the sum of their squares and use it to find the two numbers. ANSWERS: B,A,C,A,A,6C,7B,8C,9A,0D,D,D,A,C,A,6C 7D,8C,9A,0C,A,B,A,C,C,6D,7B,8A,9D,0B,D... a) f() = ( ) (b) f() = -( + ) + (c) f() = 0.(-) (d) f() = - ( ) +. (a) f() = - ( ) (b) f ( ) ( ) 6. (a) = 0. ( 6) (b) = - 0.( + 8) or ( 8) 6. (a) f() = ( ) + (b) h() =6m 7. (a) f() = -/ ( ) + 9 (b) D : 0 8, R R: 0 9, R 8. 7m X.m =.m 9. R = (60 + n) (00 0n), $ A = - + 0, Ma. Area = 900m. R = ( 0 + n) (00 n), $. 7. & 7.