Why do this problem?

This problem offers an excellent opportunity for students to gain fluency at describing the graphs of quadratic equations in a variety of ways.

Possible approach

Start by displaying the graphs of one or two quadratic equations and ask students to describe them in as much detail as possible. Expect comments related to maximum / minimum values, roots, axes of symmetry, turning points, intercepts... 

Then hand out copies of the worksheets and suggest that students work on the task in pairs.

This task could be followed up with Which Quadratic? which requires students to ask suitable questions in order to identify a quadratic.

Key questions

Do any of the graphs satisfy just one of the criteria?

Can any of the criteria be matched to just one of the graphs?

Possible support

Encourage students to consider the Key questions above

Possible extension

Parabolic Patterns challenges students to identify the equations of graphs.