Quadratic Functions and Equations in One Variable · 1.1.7
Sketching quadratic graphs
Students sketch the parabola for a given quadratic function by identifying key features: the shape from a, the turning point, the axis of symmetry, and intercepts where they exist, then draw a smooth curve without needing to plot every point precisely.
The official learning standard (1.1.7)
“Sketch graphs of quadratic functions. For quadratic functions with no real roots, limited to cases where the maximum or minimum point lies on the y-axis.”
What it means
Students sketch the parabola for a given quadratic function by identifying key features: the shape from a, the turning point, the axis of symmetry, and intercepts where they exist, then draw a smooth curve without needing to plot every point precisely.
How it is examined
Paper 2 typically asks students to sketch a quadratic graph as part of a larger question, showing the turning point and intercepts clearly. Paper 1 may test recognising a correctly sketched graph that matches a given function.
Worked example
Sketch the graph of f(x) = x² + 4, stating why it has no real roots.
- Since a = 1 > 0, the parabola opens upward.
- The function can be written as f(x) = (x − 0)² + 4, so the minimum point is (0, 4), which lies on the y-axis.
- Because the minimum value, 4, is positive, the graph never reaches y = 0, so f(x) = 0 has no real roots.
- Sketch: an upward parabola with minimum point (0, 4), symmetric about the y-axis, entirely above the x-axis.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Do I need to plot exact points to sketch a quadratic graph?
No, a sketch only needs the general shape and key features to be reasonably accurate: the correct opening direction, the turning point roughly in the right place, and intercepts marked where they exist. Exact plotting of every coordinate is not required.
How do I sketch a graph when the equation has no real roots?
Use the shape from a and the turning point, which in this standard's scope lies on the y-axis, to draw the curve entirely above the x-axis (if a > 0) or entirely below it (if a < 0). The curve does not cross or touch the x-axis at all.
What are the minimum features I must show in the sketch?
At minimum, show the correct shape and opening direction, the coordinates of the turning point, and any x-intercept or y-intercept that exists. These features are what markers look for to confirm the sketch matches the given function.