Common Mistakes When Drawing Quadratic Graphs

Drawing a quadratic graph is not difficult, but small plotting errors can make the whole parabola inaccurate. Here are the most common mistakes to avoid.

⚠️ 1. Plotting Coordinates Incorrectly

After calculating a table of values, each point must be plotted accurately.

For example:$$(2,-1)$$

means:$$x=2,\qquad y=-1$$

A small plotting error can change the position of the turning point and the shape of the curve.

---

⚠️ 2. Joining the Points with Straight Lines

A quadratic graph is a smooth curve, not a collection of straight line segments.

❌ Incorrect:

Point → straight line → point → straight line

✅ Correct:

Draw one smooth parabola passing through the plotted points.

---

⚠️ 3. Drawing a Thick or Rough Curve

Avoid repeatedly tracing over the graph.

The curve should be:

• thin
• smooth
• continuous
• accurately drawn through the plotted points

A thick curve can make values difficult to read accurately.

---

⚠️ 4. Using the Wrong Scale

Always check the scale on both axes before plotting.

For example, one square might represent:$$1$$

or:$$2$$

or another value.

Do not automatically assume every square represents one unit.

---

⚠️ 5. Missing the Turning Point

The turning point is the lowest or highest point of the parabola.

For:$$y=x^2-4x+3$$

the turning point is:$$(2,-1)$$

The curve should turn smoothly at this point.

---

⚠️ 6. Drawing the Line of Symmetry in the Wrong Position

The line of symmetry passes directly through the turning point.

If the turning point is:$$(2,-1)$$

then the line of symmetry is:$$x=2$$

It must be drawn vertically through $x=2$, not $x=2.5$ or another nearby value.

---

⚠️ 7. Confusing Roots with the Turning Point

The roots are where the quadratic curve meets the x-axis.

At a root:$$y=0$$

For:$$y=x^2-4x+3$$

the roots are:$$(1,0)$$

and:$$(3,0)$$

The turning point:$$(2,-1)$$

is not a root.

---

⚠️ 8. Forgetting the y-Intercept

The y-intercept occurs where:$$x=0$$

For:$$y=ax^2+bx+c$$

the y-intercept is:$$(0,c)$$

For:$$y=x^2-4x+3$$

the y-intercept is:$$(0,3)$$

---

⚠️ 9. Drawing an Asymmetrical Parabola

A quadratic parabola is symmetrical about its line of symmetry.

For example, if:$$x=2$$

is the line of symmetry, points the same distance from $x=2$ should have the same y-value.

For:$$y=x^2-4x+3$$

we have:$$(1,0)\qquad\text{and}\qquad(3,0)$$

and:$$(0,3)\qquad\text{and}\qquad(4,3)$$

This symmetry is a useful way to check your graph.

---

💡 Exam Tip

Before finishing your graph, quickly check:

Scale → Points → Smooth curve → Roots → Turning point → Symmetry → Axis labels

If these are correct, your quadratic graph is likely to be accurate.

⭐ Quick Summary

A good quadratic graph should have accurately plotted coordinates, a thin smooth curve, the correct scale, proper symmetry, and clearly labelled axes.

Most importantly:

Never join quadratic points using straight line segments.