Answer: To find the time that the rocket will hit the ground, we need to determine when the height of the rocket, y, reaches zero. The equation given is: y = -16x^2 + 172x + 146 To find the time when the rocket hits the ground, we set y equal to zero and solve for x: 0 = -16x^2 + 172x + 146 This is a quadratic equation in the form ax^2 + bx + c = 0, where a = -16, b = 172, and c = 146. To solve this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a) Plugging in the values for a, b, and c, we get: x = (-172 ± √(172^2 - 4(-16)(146))) / (2(-16)) Simplifying this expression gives us two solutions for x: x = (-172 ± √(29584 + 9344)) / (-32) Now, we can calculate the two possible values for x: x = (-172 + √38928) / (-32) x = (-172 - √38928) / (-32) Evaluating these expressions, we find that: x ≈ 4.73 seconds or x ≈ 8.27 seconds Therefore, the rocket will hit the ground approximately 4.73 seconds or 8.27 seconds after launch.