Quadratic inequalities
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- When is the profit positive?
- Equation first, then the range
Read the transcript of the teaching part
Last time
Before we start: last time, in The discriminant, a line and a curve, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
When is the profit positive?
A firm's profit follows a curve, going up and then back down. The question is not when the profit is zero, but for which sales it is above zero. That is a quadratic inequality, and its answer is a range of values, not a single number.
Equation first, then the range
Replace the inequality sign by an equals sign and solve. The answers are the critical values. Sketch the curve. A positive x squared term gives a smile; a negative one gives a frown. Read off where the curve is above the axis for greater than, or below for less than.
Chapter 2: Quadratic functions
- Solving quadratics and completing the square 5 min
- The discriminant, a line and a curve 6 min
- Quadratic inequalities 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.