Quadratic equations are a fundamental part of high school maths, covering everything from factorising and sketching, to completing the square and using the quadratic formula. There’s always something to challenge students and keep the class engaged.
While it may seem intense at times, understanding quadratics is key to unlocking a variety of mathematical concepts. And even if the purpose isn’t immediately clear, there’s a lot of value in learning how these principles apply to the world around us.
So, let’s explore 4 great reasons why you should embrace quadratic equations and see how they can open up new opportunities in learning and problem-solving.
You wouldn’t have an action movie
Back in the 1990’s, it wasn’t possible to use CGI in space movies. Actors ‘floated’ around in weightless conditions, fighting aliens, zapping the bad guys – by hanging on a wire dangling from a rig.
That was until the blockbuster film Apollo 13, directed by the brilliant Ron Howard. He needed high quality footage to convince the audience. So, to create lifelike and realistic scenes, real weightlessness was created by an aeroplane flying a parabolic course (a quadratic!).
You can even book the experience today. Not sure of the cost, but you get 22 seconds floating around in the cabin like Neil Armstrong.
You wouldn’t have a cellphone
Surely not! How could we ever have a life without one? Actually we owe mobiles to quadratic equations …. although it’s a little more complex.
Modern communication has a basis in quadratic equations. It was a quadratic that led to the usage of the ‘imaginary number (i).’ Within quantum theory, the imaginary number is fundamental to Schrodinger’s equation:
i (∂u / ∂t) + v²+ v(x)u = 0
This equation is very important in the design of circuits that perform signal processing – useful in cellular and wireless technologies, as well as radar and even biology (brain waves). Essentially, if the signal being measured relies on a sine or cosine wave, the imaginary number is used. And that leads to the latest iphone.
You couldn’t score the winning goal
Silence. The crowd held their breath for the final minute. The last shot of the game. Player of the year Simon Deacon grinned confidently at the crowd, before gathering his thoughts and focusing entirely on the one place the goalkeeper couldn’t quite reach.
A collective gasp as the ball curved past the waiting defenders, who could only watch in disbelief, as it landed exactly on target. The crowd went wild, as Simon Deacon won for England. The beautiful game had never looked so stunning.
And it was a quadratic equation that swerved past the losing team.
You wouldn’t scream on a roller coaster
Roller coasters are incredible feats of engineering, with some highly professional designers creating amazing thrills. Amongst the twists and turns, screaming, adrenaline-pumping, heart-stopping rides there’s bound to be a quadratic equation or two. (Maybe I should try a few roller coasters just to check).
So, what use is a quadratic equation? I could get all mathsy and talk about squared terms, plotting on a graph or finding the solution. Or how quadratics have changed our understanding of the world, tax laws, outer space, manufacturing, flight times, athletics….
So here’s a bonus answer, just because quadratic’s have made a significant impact on pretty much everything.
We couldn’t find any little green men
With many profound scientific discoveries a click away from an explanatory video, it’s sometimes good to reflect on the incredible intelligence of pioneering academic study. Amazing people who looked past the obvious, and didn’t take accepted wisdom for granted.
At one point we thought that the Earth was the centre of the universe. That was until Copernicus – around the 1500’s – used an early understanding of a quadratic equation, to propose that the Earth was actually rotating around the sun.
This thinking inspired Johannes Kepler, considered by many to be the father of modern astronomy, to develop the idea of elliptical orbits … and paved the way for our understanding of the solar system.
Although he didn’t quite live to see it, Kepler predicted that the planet Venus would pass in front of the sun (called a ‘transit’) as early as 1631. This is a rare event — only 52 in around 400 years — but it leads to calculating the distance between the Earth and the sun.
And, amazingly, the realisation that most planets have an atmosphere.
A quadratic equation gave us a tool to calculate how planets moved but, more importantly, it can help to predict where they are likely to be. Space is big. Finding a planet can be quite challenging … it really helps to know where they are at any given point.
That’s not all. A quadratic equation enabled us to see the planets like never before. The philosopher, mathematician and astronomer Galileo (1564–1642) made a significant contribution to the development of telescopes, using two intersecting mirrors, each in the shape of a hyperbola. With Galileo’s painstaking commitment to improvement, the telescope was eventually able to magnify the surface of the moon, in some considerable detail.
Until that point, most thought the moon was smooth and polished. Imagine Galileo’s surprise when he found that, in his own words, it was “uneven, rough, full of cavities and prominences.”
Also using a ‘quadratic curve,’ Newton designed his reflecting telescope, with parabola shaped mirrors, and the design has stayed with us today.
Without these inventions, we’d have a very hard time trying to see the solar system with any precision … and there might be little green men just waiting to say hello.
So, there you have it. Quadratic equations, and our understanding of them, have shaped all aspects of our lives. From your bathroom mirror, to an intergalactic council meeting, it’s quite likely that a quadratic was involved.
I hope you enjoyed this slightly irreverent post on a very powerful maths equation… if you did, please consider sharing or adding a comment … it really helps to persuade the algorithm to share with others. Thank you!
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