Final answer:
To model the path of the frog's jump, we use a quadratic function of the form y = ax^2 + bx + c. By substituting the given values for the highest point and horizontal distance, we can find the values of a and b, resulting in the quadratic function y = -¼x^2 + ½x.
Step-by-step explanation:
To model the path of the frog's jump, we can use a quadratic function of the form y = ax^2 + bx + c, where y represents the vertical position and x represents the horizontal position. We are given that the frog starts at (0,0), so we can substitute these values into the quadratic function. Since the highest point of the jump is ³ ¹ / ² foot, we can substitute this value for y when x = 1 foot to find the value of a. We can also substitute the fact that the frog leaps 2 feet horizontally when x = 2 to find the value of b. Finally, since the frog starts at (0,0), we know that c = 0. Therefore, the quadratic function that models the path of the frog's jump is y = -¼x^2 + ½x.