Sketching curves, tangents and turning points
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- The top of the roller coaster
- Sketch versus plot
- Sketching a quadratic
Read the transcript of the teaching part
Last time
Before we start: last time, in Graphs of functions, tangents and turning points, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
The top of the roller coaster
On a roller coaster the track climbs, reaches the top, and then drops. At the very top the track is flat for an instant: the gradient is zero. That is a turning point. Today you sketch curves with their key points, find the gradient of a curve at any point using a rule, and use that rule to find the top or bottom.
Sketch versus plot
A sketch is a quick picture with no scale. It must show the right shape and label the key points. The key points are where it crosses the axes and where it turns. Mark their coordinates. Never use a ruler on a curve, and do not make a quadratic pointed.
Sketching a quadratic
It is a U shape, because x squared is positive. Find where it crosses the x-axis: factorise to x minus one, times x minus three. So it crosses the x-axis at one and three. The y-axis crossing is where x is zero: y is three. The turning point is halfway between the roots, at x equals two. Then y is four minus eight plus three: minus one.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Sketching curves and turning points.
The whole chapter: Graphs of Functions and Sketching Curves.
Chapter 15: Graphs of functions
- Drawing graphs and solving equations graphically 5 min
- Sketching curves, tangents and turning points 6 min
Also for IGCSE Maths 0580
Which topics come up most in IGCSE Maths 0580 past papers, counted from every paper since 2004.