Comparing a Straight Line and a Curved Shape: Linear vs. Quadratic Functions
Similarities:
• Starting Point: Both of these functions start from the point where the graph crosses the x-axis (the horizontal line) and the y-axis (the vertical line). This point is called the origin (0, 0).
• Never-Ending: These functions keep going forever, without stopping. They stretch out towards both positive and negative infinity, which is like saying they never run out of numbers to work with.
Differences:
• Shape: Think of a straight-line graph like going up a gentle hill. That’s what a linear function is like. Now, picture a graph that makes a curved shape, sort of like a smiley face. That’s what a quadratic function looks like.
• How They Change: When you look at the straight-line graph, it changes at a steady pace. But the curved one changes in a more interesting way, with some parts changing faster than others.
• How Far They Reach: The straight-line graph can keep going up and down forever. The curved graph can also stretch out endlessly, but it might have a limit where it stops going higher or lower, depending on how it’s smiling or frowning.