Functions & Graphs

CoreMaths revision

Linear and Quadratic Graphs

Compare line and parabola behaviour using equations, intersections and models.

Open calculator

Focus points

✓Find intersections.

✓Interpret tangency.

✓Compare linear and quadratic change.

orin

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions

Question 1FluencyCore

Original practice · Free Online Revision

Skill · intersection

Find intersections of y=x²−1 and y=x+1.

Question 2FluencyCore

Original practice · Free Online Revision

Skill · tangency

How many intersections do y=x²+4 and y=4x have?

Question 3FluencyCore

Original practice · Free Online Revision

Skill · parameter tangency

Find k so y=x² and y=2x+k touch.

Question 4ReasoningCore

Original practice · Free Online Revision

Skill · growth comparison

State which eventually grows faster for large positive x: y=5x+100 or y=x².

Question 5FluencyCore

Original practice · Free Online Revision

Skill · intersection

A line y=3x−2 intersects y=x²−6 at two points. Find x-coordinates.

Question 6ApplicationCore

Original practice · Free Online Revision

Skill · model intersection

A projectile height is h=−x²+6x. A horizontal wall top is y=5. At what x-values is projectile at wall height?

Question 7ReasoningCore

Original practice · Free Online Revision

Skill · reasoning

Explain why a line can intersect a parabola at at most two points.

Question 8ChallengeStretch

Original practice · Free Online Revision

Skill · consistency challenge

Find the line y=mx tangent to y=x²−4 at a point with positive x.