Reach for the Star | GCSE Mathematics

L058: Quadratic graphs and roots

Objective

Plot quadratic graphs and interpret roots and key features.

Calculator: Calculator allowed where labelled; non-calculator reasoning remains required.

Visual model for Quadratic graphs and roots
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for quadratic graphs and roots.

Core practice

For y=x²−4x+3, find both roots and the turning point.

Reasoning

A quadratic has roots −1 and 5. Write a monic equation and state its axis of symmetry.

Exam-style

A graph is drawn for a real context. Interpret the gradient, intercept or area as appropriate. State units and justify your answer.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L058: Quadratic graphs and roots

Objective: Plot quadratic graphs and interpret roots and key features.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.

Even Better If (EBI)

I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.

Stretch and deep challenge

Stretch: For y=x²−4x+3, find both roots and the turning point.

Deep challenge: A quadratic has roots −1 and 5. Write a monic equation and state its axis of symmetry.