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CAS Mathematics 1.2 Demonstrate an understanding of the features of graphs

Quadratic functions written in any form

In the equation y = kx², the number k in front of the x² means that the shape of the parabola changes.

If k is greater than one, e.g. y = 3x², the parabola will be steeper.

If k is less than one, e.g. y = x², the parabola will be flatter.

For more information on quadratics with a coefficient of x² other than ±1, see:
The meaning of the leading coefficient

Quadratic functions (Java™ required)

Slider graph (Java™ required)

An activity using TI-nspire CAS™ for mathematics achievement standards 1.1, 1.2, 2.1, 2.2

Writing equations

For excellence, assessment may involve writing equation(s) from a graph to solve a problem in context. For writing quadratic equations, a combination of two different types of transformations only is expected, eg y = 2x² + 3, or y = (x-2)² + 1.

If you are given a graph and asked to find its equation you firstly need to look at the coordinates of the vertex. If the vertex is at point (1,2) then you know that the graph of y = ax² (equation 1) has been translated 1 unit horizontally and 2 units vertically.

Therefore the equation is:
(y-2) = a(x-1)² (equation 2).

All you need to do now is work out the value of ‘a’. Do that by choosing some other point on the parabola (not the vertex) and substitute its coordinates into equation 2. You can then work out the value of ‘a’ and complete your equation.

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