Types-Of-Graphs Aqa Foundation

Types of graphs

What graphs do I need to know?

• You need to be able to recognise the following lines:

  •  Straight lines

    • y = mx + c

    • Such as y = 3x  + 2, y = 5x  – 1, …

    • Two important ones are y = x and y = –x

  • Horizontal lines

    • y = c

    • Such as y = 4, y = -10, …

  • Vertical lines

    • x = k

    • Such as x = 2, x = -1, …

• You need to be able to recognise quadratic graphs

  • y = x²

  • y = –x²

  • y = ax² + bx + c

• You need to be able to recognise simple cubic graphs

  • y = x³

  • y = –x³

  • y = ax³ + bx² + x + c

• You also need to be able to recognise reciprocal graphs

  • , where 

What does a quadratic graph look like?

• The equation of a quadratic graph is y = ax² + bx + c

• A quadratic graph has either a u-shape or an n-shape

  • This type of shape is called a parabola 

• u-shapes are called positive quadratics

  • because the number in front of x² is positive

    • For example, y = 2x² + 3x + 4

• n-shapes are called negative quadratics

  • because the number in front of x² is negative

    • For example, y = -3x² + 2x + 4

• You can plot quadratic graphs using a table of values
   

What does a cubic graph look like?

• The equation of a cubic graph is y = ax³ + bx² + cx + d

• A cubic graph can have two points where it changes direction (turning points)

• A positive cubic goes uphill (from the bottom left to the top right)

  • The number in front of x³ is positive

    • For example, y = x³ – 3x² + 2x + 1

• A negative cubic goes downhill (from the top left to the bottom right) 

  • The number in front of x³ is negative

    • For example, y = –x³ + 2x² – x + 5

• You can plot cubic graphs using a table of values

What does a reciprocal graph look like?

• The equation of the basic reciprocal graph is 

  • You cannot substitute in x = 0 (division by zero is not allowed) 

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