Types of Graphs (Cambridge (CIE) IGCSE Maths)

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 also need to be able to recognise reciprocal graphs

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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 are the key features of a quadratic graph?

• The point where the graph turns is called the vertex

  • Positive quadratics have a minimum point

    • The bottom of the u-shape

  • Negative quadratics have a maximum point

    • The top of the n-shape

• Quadratic graphs always have a vertical line of symmetry down the middle

  • The equation of the vertical line of symmetry is  x = k

    • k is the x-coordinate of the minimum or maximum point

• Quadratic graphs do not have to cross the x-axis

  • If they do, two x-intercepts are created, called roots

    • If the curve just touches the x-axis, only 1 root is created

  • Roots are symmetric about the vertical line of symmetry

• Quadratic graphs always have one y-intercept

What does a reciprocal graph look like?

• The equation of a reciprocal graph is 

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

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  • You should not include x  = 0 in a table of values

• The shape of is shown below (for a positive value of a)

  • It has two two curved branches

    • The branches are L-shaped

    • The L is more rectangular when a  is smaller

  • The branches never connect!

• A negative value of a  reflects the shape in the y-axis