What this guide covers
Selected Sec 2 N6 graph features: symmetry, turning point and direction of opening. Later sketching of completed-square forms and curve-tangent gradients are outside this lesson.
Read the paired values
If two plotted points have the same y-value, their x-values may lie on opposite sides of the symmetry line. The line halfway between them passes through the turning point. Check whether the vertex is a maximum or minimum.
Locate a maximum from a table
A quadratic graph has points (−1,0), (0,3), (1,4), (2,3) and (3,0). Identify its line of symmetry, turning point and the displayed x-intercepts.
- The y-values at x=0 and 2 match, and those at x=−1 and 3 match. Both pairs are centred at x=1.
- The point (1,4) is the highest of the listed points, so the symmetry line is x=1 and the turning point is a maximum at (1,4).
- The displayed x-intercepts are (−1,0) and (3,0).
Check: The two intercept x-values are equally far from 1, which agrees with the symmetry line.
Try it yourself
Work on paper, then compare the steps. These checks do not establish mastery.
A quadratic graph has values y=3, 0, −1, 0, 3 at x=0,1,2,3,4 respectively. State its symmetry line and turning point.
Pairs x=0 and 4, then x=1 and 3, match. They are centred at x=2, where y=−1 is the minimum. Symmetry line x=2; turning point (2,−1).
A quadratic graph opens downwards and has turning point (2,7). Is 7 a maximum or minimum y-value? What happens to y as x moves away from 2 on either side?
It is a maximum. Moving away from the symmetry line x=2 on either side makes y decrease. Opening direction, not the point's positive height, determines maximum versus minimum.
Where this connects
- Earlier: straight lines →
Compare a constant gradient with a curve whose steepness changes.
- Later: equations and graph intersections →
The Upper Secondary guide connects quadratic features to exact algebraic solutions.
Sources and scope
Original Mentora tables and questions aligned to selected Sec 2 N6 content in the MOE G2/G3 Mathematics syllabus. No school graph or paper item was copied.