Year 10 Interactive Maths - Second Edition

Graphs of y = ax² + c, a > 0

Example 5

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 y-axis.  So, the equation of the axis of symmetry is x = 0.
The minimum value of  y is 3 and it occurs when x = 0.
The vertex of the parabola is the point (0, 3).

In general:

Graphs of y = ax² + c, a < 0

Example 6

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 downwards.  Clearly, the graph is symmetrical about the y-axis.  So, the equation of the axis of symmetry is x = 0.
The maximum value of  y is 1 and it occurs when x = 0.
The vertex of the parabola is the point (0, 1).

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 ]