The key difference between a linear and a quadratic line lies in their visual representation on a graph: linear graphs form straight lines, while quadratic graphs create a U-shaped curve called a parabola.
Understanding Linear Graphs
Linear equations, when plotted on a graph, always produce a straight line. This line can slope upwards (positive slope), downwards (negative slope), or be horizontal (zero slope).
Key characteristics of linear graphs:
- Straight line: The relationship between x and y values is constant.
- Constant rate of change: The slope of the line is constant throughout.
- Simple equation: They are described by equations of the form y = mx + c, where 'm' is the slope, and 'c' is the y-intercept.
Understanding Quadratic Graphs
Quadratic equations, on the other hand, produce a curved line called a parabola. This parabola can open upwards (U-shape) or downwards (inverted U-shape).
Key characteristics of quadratic graphs:
- Parabolic curve: The graph has a U- or inverted U-shape.
- Non-constant rate of change: The slope of the curve changes along its length.
- Equation with a squared term: Quadratic graphs are represented by equations like y = ax² + bx + c, where 'a' determines the direction and width of the parabola.
Comparison Table
| Feature | Linear Graph | Quadratic Graph |
|---|---|---|
| Shape | Straight line | Parabola (U-shaped curve) |
| Rate of change | Constant | Non-constant |
| Equation form | y = mx + c | y = ax² + bx + c |
| Visual Example |  |
 |
As clearly stated in the provided reference, "Linear graphs always look like a straight line with no curve." In contrast, "Quadratic graphs have a parabola shape." This distinction makes it easy to identify and differentiate between the two when looking at a graph.
