Quadratic Graphs – Building a Table and Plotting the Curve
Graphing a quadratic equation follows the same table-plot-draw approach you used for straight lines, with one key difference: because the curve bends, you need more points – typically five or more spread across a range of x-values – to see its true U-shape rather than a jagged approximation. Choosing x-values on both sides of the curve's centre is especially important, so the symmetry of the parabola is clearly visible.
One easy point to find without any table at all is the y-intercept: exactly as with a straight line, it's simply the value of c, found by setting x = 0.
Building a Quadratic Table of Values
Choose several x-values, calculate y = ax² + bx + c for each, plot the points, and draw a smooth curve through them. The y-intercept is always c.
y = 4² − 2(4) − 3 = 16 − 8 − 3 = 5.
At x = 0: y = 2(0)² + 5(0) − 7 = −7.
Real-Life Application
- Trajectory modelling: plotting a projectile's height over time as a curve.
- Engineering design: plotting stress or load curves that follow a quadratic pattern.
- Profit modelling: plotting how profit changes with price as a curve.
Key Takeaways
- Graphing a quadratic uses the same table-plot-draw method as a line, with more points.
- Points on both sides of the curve's centre reveal its symmetric shape.
- The y-intercept of a quadratic is always c.
Practice: Quadratic Graphs
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