A quadratic function or equation has the form f(x) = ax2 + bx + c. It contains three terms:
- ax2 = the quadratic term (a is the leading coefficient). This term is always raised to 2, so is sometimes called the squared term.
- bx = the linear term,
- c = the constant term.
- A positive coefficient will result in a “U” shape,
- A negative coefficient will result in a “∩” shape.
It’s called a quadratic term because it’s the term that makes the expression a quadratic function: take away the “ax2” and you’re left with a linear function bx + c.
Quadratic Term Example
Projectile motion can be described by, in part, a quadratic term. For example, the following graph shows the path of a baseball:
The expression needed to fully explain the baseball’s path has three parts:
- The quadratic term represents the ball’s motion due to gravity. That’s what gives the path the distinctive quadratic (i.e. humped) shape: acceleration slows down as gravity pulls on the ball. Eventually the ball reaches its peak height, then gravity slows the ball down further until it eventually hits the ground.
- The linear term represents the vertical (upwards) motion of the ball after it is hit by the bat. This part of the expression would be a straight line, except that gravity bends it downwards.
- The constant term represents the ball’s initial height when hit. For a baseball, this would be roughly 2-3 ft, depending on the height of the player.
Next: Quadratic approximation.
Stephanie Glen. "Quadratic Term: Definition, Examples" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/quadratic-term-definition-examples/
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