MCR3UE Unit Test: Quadratic Functions K= /16 A= /17 C= /3 Name: Total /4 /40 T= Part A: Multiple Choice (circle the best answer for each question) [K=5] Which of the following is true about the parabola for the function ? a The y-intercept is c The axis of symmetry is x = – b The vertex is (4, 5) d The parabola opens down What the parabolas a and They have the same y-intercept c have in common? They have the same x-intercepts b They have the same vertex They have the same axis of symmetry d Which of the following quadratic functions will have a minimum value? a b c d Which of the following are roots of the equation a x = –4, c b x = –28, d ? x = –7, x = –24, What is the value of the discriminant for the function a –68c b –55 ? c 393 Input your answers here for the above multiple choice questions d Part B: Short answers Show steps for full marks (a) Given a function y 3x 12 x , rewrite the function in vertex form by completing the square [K=3] MCR3UE (b) Graph the function and indicate the vertex and two other points on the graph Label the graph properly [K=3] (c) State and range of the function Determine the roots of the equation found your answer the domain [K=2] by factoring Explain how you [C=3] Use the quadratic formula to determine each of the roots of – 7x2 – 23x + 10 = to two decimal places [K=3] MCR3UE Determine algebraically the coordinates of the point(s) of intersection of the system and [A=4] 10 Write the equation of the quadratic function given the x-intercepts are and , and a point 3, 24 is on the parabola [A=4] 11 Find the value(s) of k so that the graph of the function f x 2 x kx 50 has one x-intercept (root) [A=4] MCR3UE 12 The cost function for a telephone manufacturing plant is C(x) = 4x + 169 and the revenue function is R(x) = –2x2 + 48x, where x is the number of telephones sold, in thousands a) Determine the profit function for the number of phones sold b) Determine the number of telephones sold that maximizes profit c) Determine the maximum profit in thousands [A=5] 13 A model rocket is launched off the top of a table The height of the rocket is given by the function, h(t) = - 4.9t2 + 9.5t + 1.2 where h(t) is the height in metres and t is the time in seconds How long will it take for the rocket to reach the ground? Answer in decimal places [T=4] MCR3UE ... domain [K=2] by factoring Explain how you [C =3] Use the quadratic formula to determine each of the roots of – 7x2 – 23x + 10 = to two decimal places [K =3] MCR3UE Determine algebraically the coordinates...MCR3UE (b) Graph the function and indicate the vertex and two other points on the graph Label the graph properly [K =3] (c) State and range of the function... intersection of the system and [A=4] 10 Write the equation of the quadratic function given the x-intercepts are and , and a point 3, 24 is on the parabola [A=4] 11 Find the value(s) of k so