Types of Graphs

What are the shapes of graphs that you need to know?

Below are the basic form of graphs you need to recognise:
- horizontal line (y = a) and vertical line (x = a)
- linear ( $y = \pm x$ , y = mx + c)
- quadratic ( $y = \pm x^{2}$ , y = ax² + bx + c)

What does a quadratic graph look like?

A quadratic graph has the form $y = a x^{2} + b x + c$
The shape made by a quadratic graph is known as a parabola
The parabola shape of a quadratic graph can either look like a “u-shape” or an “n-shape”
- A quadratic with a positive coefficient of $x^{2}$ will be a u-shape
  - e.g. $y = x^{2} + 2 x + 3$
- A quadratic with a negative coefficient of $x^{2}$ will be an n-shape
  - e.g. $y = - x^{2} + 2 x + 3$
A quadratic will always cross the $y$ -axis
A quadratic may cross the $x$ -axis twice, once, or not at all
- The points where the graph crosses the $x$ -axis are called the roots
If the quadratic is a u-shape, it has a minimum point (the bottom of the u)
If the quadratic is an n-shape, it has a maximum point (the top of the n)
Minimum and maximum points are both examples of turning points
Quadratic graphs have a vertical line of symmetry
- the equation of the vertical line of symmetry is x = k where k is the x-coordinate of the minimum or maximum point

Quadratic Graphs Notes Diagram 1

Worked example

Which graph below is the only possible graph of $y = - x^{2} + 3 x + 2$ ?

A quadratic graph is either a U or ∩ shape
The negative coefficient of x² in y = -x² + 3x + 2 (the number before x², in this case -1) means it is an ∩ shape

Graph C

Types of Graphs (CIE IGCSE Maths: Core)

Revision Note

Types of Graphs

What are the shapes of graphs that you need to know?

What does a quadratic graph look like?

Worked example

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Author: Mark