Samantha is creating a smartphone game for young children where online players are squirrels, playing ‘catch’, by throwing an acorn between them. The trajectory of an acorn, after it is thrown by a squirrel, is modelled in the computer code by a quadratic equation of the form y = ax2 bx c, where y represents the height (in metres) of the acorn above the ground, and x represents the horizontal distance (in metres) of the acorn from the position where it was launched. The values of a, b and c are determined by how a squirrel launches an acorn. You may assume that the surface where the squirrels are standing is completely flat and horizontal. Samantha is running a simulation of the game between two squirrels called Hazel and Poppy, who are standing two metres apart. The squirrels can jump vertically to catch an acorn if required. The equation produced to model the trajectory of an acorn when Hazel throws it to Poppy is y = −0.46x 2 0.98x 0.18. When the acorn is directly above Poppy’s position, she can catch it without jumping if it is no more than 0.2 metres above the ground. Will Poppy need to jump in order to catch the acorn? Explain your reasoning.
