A quadratic is an equation whereby the highest exponent of the variable is 2; the graph of which forms a parabola.

A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus) and a fixed straight line (a directrix).

Exploring the shapes of graphs using technology

Maths

Checking and securing understanding of non-linear sequences

Extending thinking about sequences

Equations and their graphs

Efficiently drawing linear graphs

Reading from graphs

Modelling with graphs

Graphically solving two linear graphs that intersect

Problem solving with graphical representations

In this unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In the future unit, other types of graphs are introduced and their key features identified.

In the prior unit, pupils considered geometric sequences and how they might be represented graphically. In this unit, pupils study the graphical representation to link features of the graph to its equation.

In this unit pupils draw, interpret and utilise linear graphs to solve problems. This knowledge is further extended to look at intersecting graphs.

Graphical representations

A __________ equation is an equation where the highest exponent of the variable is 2.

__________ is a special symmetrical curve which can be bowl-shaped or archlike.

Which of the below equations will form a parabola when plotted?

Match each equation to the description of its shape when graphed.

Which of these equations will produce parabolas that are 'archlike' or appear to 'open downwards' when graphed?

The linear equation $$y=3x-7$$ will form a __________ graph.

Which of these coordinates will be on the linear graph $$y=3x-7$$?

The number of points you can plot on this graph goes on infinitely.

How many points can be plotted on the graph of the linear equation $$y=3x-7$$?

If you were populating this table of values for the linear equation $$y=8-5x$$, what is highest value of $$y$$ you will get?

If you were populating this table of values for the linear equation $$y=8-5x$$, what is lowest value of $$y$$ you will get?

Which of these equation will produce a non-linear graph?

Exploring the shapes of graphs using technology

Lesson outcome