When you superimpose a grid onto Pete’s punt, you find that on a typical punt, the ball lands a full 44m in front of Pete. His typical punt goes 15 m in the air. 

a) Create a quadratic equation in factored form to relate “h(x)” (the height of the ball) to “x” (the ball’s horizontal distance from Pete). HINT: The roots are where the ball starts and ends. Then use your ‘typical punt’ values to find ‘a’ for your equation.

b) Pete wants to kick the ball over the goal posts, the crossbar of which is 3.3 m in the air. If he is using this typical kick, what’s the furthest he can stand from the goalposts and still get the ball over? What’s the closest he can stand?