2.5.4

Turning Points

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Turning Points

The turning point on a line is the point where the line changes direction.

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Turning point

  • It is the point where the graph changes from sloping downwards to sloping upwards.
  • The turning point here is (3, 1).
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Complete the square

  • To find the turning point, complete the square to give y = (x - a)2 + b then the turning point has coordinates (a, b).
  • The equation y = (x - 3)2 + 1 is shown here.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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