Quadratic functions describe motions like a thrown ball's trajectory (parabola), car braking distances, and satellite dish shapes. They are fundamental in physics, engineering, and optimizing curves.
Unlike linear functions that grow at a steady rate, quadratic functions have a variable 'x' that is squared. This means as 'x' grows, 'y' grows much faster, creating a curved U-shape called a parabola.
A common mistake is forgetting that squaring a negative number results in a positive number. For example, (-3)² is 9, not -9. This is why the graph curves upwards on both the left and right sides (when a > 0).
Adjust the value of 'a' to see how the parabola y = ax² changes its shape and direction.
Test your understanding of parabolas!
Telescopes and satellite dishes use parabolic mirrors. Because of a mathematical property of the parabola, all incoming parallel rays of light or radio waves bounce off the curve and hit a single 'focal point', creating a strong signal!