Use a graphing display calculator (GDC) to graph , then apply its maximum, minimum, zero, or intersection command. Report maxima and minima as coordinate points, intercepts as coordinate points, and zeros as -values.
This is IB Mathematics: Analysis and Approaches SL 2.4, which focuses on determining key features of graphs using technology, typically in a Paper 2 setting.
| Feature | Meaning and method |
|---|---|
| Maximum | A highest point on the stated domain. Use the GDC maximum command and give ((x,f(x))). |
| Minimum | A lowest point on the stated domain. Use the GDC minimum command and give ((x,f(x))). |
| -intercept | A point where the graph crosses or touches the -axis. Solve and write . |
| -intercept | The point where . Calculate and write . |
| Zero | An -value satisfying . It is the -coordinate of an -intercept. |
For example, consider
The zeros are and , so the -intercepts are and . Since , the -intercept is .
The vertex occurs at , where . Therefore, the graph has a minimum at . It has no maximum because the parabola increases without bound.
Before using a GDC, identify the required domain. A graph can have a local maximum or minimum without having an absolute maximum or minimum over its full domain. Restrict the calculator window or set bounds around the turning point carefully; otherwise, the command may locate a different feature or return no result. For intercepts, use the zero command rather than estimating from pixels on the screen.
A common misconception is that a zero and an -intercept are written identically. A zero is , while the corresponding intercept is the point .
Exam technique: Write the equation or function entered into the GDC, ensure the viewing window shows all relevant features, and give answers exactly or to three significant figures unless instructed otherwise. Always distinguish between an -value and a coordinate point.