Year 9 Interactive Maths - Second Edition

Graphs of y = a(x-b)², a > 0

Example 7

Solution:

When we plot these points and join them with a smooth curve, we obtain the following graph.

Note:

The graph is a parabola which opens upwards.  Clearly, the graph is symmetrical about the
line x = 1.  Therefore, the equation of the axis of symmetry is x = 1.
The minimum value of  y is 0 and it occurs when x = 1.
The vertex of the parabola is the point (1, 0).

In general:

In the example above, a = 1 and b = 1.

Study Another Topic in Chapter 10: Quadratic Equations and Graphs

[ Quadratic Equations ] [ Equations Involving Factorisation ] [ Problem Solving ] [ Parabolic Graphs ] [ Graphs of y = ax² + c, a > 0 ] [ Graphs of y = a(x-b)², a > 0 ] [ Quadratic Graphs by Transformations ] [ Translation ] [ Problem Solving Unit ] [ Projects ] [ Symbols ] [ Index ]