2. Given f(x) = 3x2 + 12x + 96, state the following: a) Direction of opening. (D b) The y-intercept, in coordinate form. c) The zeros, or x-intercepts, in coordinate form. Show steps to receive process marks. d) The equation for the axis of symmetry. Show steps to receive process marks. e) The coordinate of the vertex. Show steps to receive process marks. (2) f) The max/min value. (D g) The domain and range, in proper set notation. (2) 5. Given the quadratic function f(x) = 20: + 4)2 + 3, ) Determine the equation of the inverse. Show all steps to receive process marks. 6) ) Is this inverse a function? Why or why not? Explain. ) Restrict the domain of f(x), so that the inverse is a function. (D ) a b c d Evaluate the value of the inverse when x = 5. Show all steps to receive process marks. (3) 6. Determine the value of k such that the quadratic f(x) = 2x2 5x + 3 intersects the linear function 90:) = 3x + k at exactly one point. Show full steps to receive process marks. 6) 7. State the equation of a parabola that is a member of the family of each of the following types of parabolas. G) y=3(x2)(x+5) y=(x+4)29 y=5x2+8x9 8. Determine the equation of the quadratic with a vertex (-1,-5) and passes through the point (2,-41). Show full steps to receive process marks. @ 9. A model rocket is launched from the roof of a building. Its flight path through the air is modelled by Mr) = 5t2 + 30t + 23, where h(t) is the height ofthe rocket above the ground in metres, and t is the time in seconds, after it was launched. a) How tall is the building? b) When will the rocket reach the height Of 60m? @ Round to 1 decimal place. Show full steps to receive process marks. 10. A large car dealership has been selling used cars for $12000 each. Sales have been averaging 50 cars per month. Because of inflation, the price of a used car is going to be increased. The marketing manager has determined that for every $500 increase, there will be one less car sold each month. What should the new price be to maximize revenue? 6) Let x represent the number of $500 increases and let R represent the revenue. 4. The profit function for a business is given by the equation P(x) = %x2 + x + 5 , where x is the number of items sold, in thousands. and P(x) is the dollars in thousands. CaICUlate the maximum prot and how many items must be sold to achieve it. Show all steps to receive process marks.