Please do not skip any step, I'd appreciate it very much, please leave the whole explanation as my goal is to understand these questions, if you can do that I will thank you with a super high rating

6. Determine the values of k for which the function y = 3x2 - 4x + k will have no roots. 7. Determine the points of intersection of the line x + y = 6 and the parabola given by y = -3x2 + 10. 8. The height of a rocket, in metres, above the ground is modelled by h(t) = -2t? + 24t, where t is time in seconds after the rocket is launched. Answer the following questions using the processes that you learn in this unit. Make sure to show ALL STEPS of your work. a) For how long will the rocket be in the air? b) How high will the rocket be after 3 seconds? c) What is the maximum height that the rocket will reach? At what time will this happen