A sketch with roots and a turning point

Choose your method, connect the parts and explain your conclusions. These original questions include written reasoning and sketches as well as exact answer checks.

Suggested marks guide how much working to show. The site does not automatically award examination marks for proofs, diagrams or methods. Use scaffolded fluency practice when you need a hint first.

Level 2 / FSMQ. Course filters use selected objective mappings; none of these tasks establishes complete paper coverage.

Before you start

Stationary points. Read the relevant method, then decide which parts you can solve without hints.

Check a misconception first · Try a connected problem

Read an original example question

The curve has equation y = $x^{2}$ - 4*x + 3.

Blank coordinate axes for a sketch; draw in your own working.

Part a

Find the two x-intercepts, in increasing order.

Part b

Find the turning point.

Part c

Sketch the curve, labelling its intercepts and turning point.

Model solution and review criteria

Part a

Complete the square: y = (x − 2)² − 1. Set y = 0.

Obtain a factorisation or completed square.
Give both intercepts.

Part b

The squared term is least at x = 2; y = −1.

Identify the minimum of the squared term.
Give both coordinates.

Part c

An upward-opening parabola has vertex (2, −1), x-intercepts 1, 3, y-intercept 3 and symmetry line x = 2.

Show an upward-opening curve and the correct symmetry.
Label both x-intercepts, the y-intercept and vertex.
Keep the turning point below the x-axis.

Compare your own reasoning. No automatic examination marks are awarded.