The general form of a quadratic equation is ax² + bx + c = 0 with x as a variable and a, b and c are constants. The quadratic equation can be applied to many real life examples including finding the stopping distance of a car or how to kick a perfect drop goal in a rugby match.

Working out trajectories in projectile motion, or to put it more simply relating time to distance, is used in the science of ballistics, which examines the effect of gravity on moving objects.

Using the quadratic formula which relates time to distance it is possible to work out exactly which angle to kick a rugby ball in order to score the perfect drop goal. You must work out the angle and the velocity correctly so that when it goes a distance (x) to the goal it is at the correct height (y) for it accurately clear the post.

So to take it from the beginning, the ball falls in the direction (y) with a steady acceleration (g). It travels straight in the (x) direction at a constant velocity. So if the ball starts at x = y = 0 with velocity (u) in the (x) direction and travels upwards at velocity (v) then you will be able to work out the position of the ball at time (t) by: X = ut and y = vt - 1/2gt².

This is known as a parabolic equation and is also used by the army for missile calculations. For more real life examples and explanations of quadratic equations check out the ‘101 uses of a quadratic equation’ at: plus.maths.org/content/os/issue29/features/quadratic/index

Working out trajectories in projectile motion, or to put it more simply relating time to distance, is used in the science of ballistics, which examines the effect of gravity on moving objects.

Using the quadratic formula which relates time to distance it is possible to work out exactly which angle to kick a rugby ball in order to score the perfect drop goal. You must work out the angle and the velocity correctly so that when it goes a distance (x) to the goal it is at the correct height (y) for it accurately clear the post.

So to take it from the beginning, the ball falls in the direction (y) with a steady acceleration (g). It travels straight in the (x) direction at a constant velocity. So if the ball starts at x = y = 0 with velocity (u) in the (x) direction and travels upwards at velocity (v) then you will be able to work out the position of the ball at time (t) by: X = ut and y = vt - 1/2gt².

This is known as a parabolic equation and is also used by the army for missile calculations. For more real life examples and explanations of quadratic equations check out the ‘101 uses of a quadratic equation’ at: plus.maths.org/content/os/issue29/features/quadratic/index