Root: A root of f(x) = 0 is an x-value where the graph crosses or touches the x-axis.
- x-intercept value
Root is usually an x-value: The x-intercept point is (root, 0), but the root itself is the x-coordinate.
| Task | Tool |
|---|---|
| Show graph | graphing mode |
| Locate x-axis crossing | root/zero tool |
| Refine estimate | move near the crossing |
Worked example
A graph crosses the x-axis near x = 1.73. What is the approximate root?
Step by step
- The root is the x-value at the x-axis crossing.
Final answer
x ≈ 1.73
Never wonder what to study next
Get a personalized daily plan based on your exam date, progress, and weak areas. We'll tell you exactly what to review each day.
Try Free Study Plan7-day free trial • No card required
| Graph behaviour | Root information |
|---|---|
| Crosses x-axis three times | three real roots |
| Touches and turns | still a root there |
| Never reaches x-axis | no real roots visible |
Count carefully: A polynomial may have more than one real root, so scan the whole visible graph.
Worked example
The calculator gives x = -2.418736 as a root. Report it to 3 significant figures.
Step by step
- Round the x-value only.
Final answer
x ≈ -2.42
Approximate means approximate: If the question asks for an approximate root, use a rounding symbol or wording like 'approximately' when helpful.