Year 10 Interactive Maths - Second Edition

Graphs of y = a(x - b)², a > 0

Example 7

Solution:

Note:

The graph is a parabola which opens upwards.
The graph is symmetrical about the line x = 2. So, the equation of the axis of symmetry is x = 2.
The minimum value of y is 0 and it occurs when x = 2.
The vertex of the parabola is (2, 0).

In general:

Graphs of y = a(x – b)², a < 0

Example 8

Solution:

Note:

The graph is a parabola which opens downwards.
The graph is symmetrical about the line x = 2. So, the equation of the axis of symmetry is x = 2.
The maximum value of y is 0 and it occurs when x = 2.
The vertex of the parabola is (2, 0).

In general:

Study Another Topic in Chapter 13: Quadratic Graphs

[ Quadratic Functions ] [ Graphs of y = ax² + c, a > 0 ] [ Graphs of y = a(x - b)², a > 0 ] [ Graphs of y = a(x - b)² + c, a > 0 ] [ Quadratic Graphs by Transformations ] [ Translation ] [ Sketching Parabolic Graphs ] [ Problem Solving I ] [ Quadratic Inequalities ] [ Simultaneous Equations - Linear/Quadratic ] [ Problem Solving II ] [ Sketching Quadratic Inequalities ] [ Intersection of Half-Planes ] [ Problem Solving Unit ] [ Projects ] [ Symbols ] [ Index ]