L058 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.
For y=x²−4x+3, find both roots and the turning point.
Roots 1 and 3; y=(x−2)²−1, turning point (2,−1).
A quadratic has roots −1 and 5. Write a monic equation and state its axis of symmetry.
y=(x+1)(x−5)=x²−4x−5; axis x=2.
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.
I represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.
I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.
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.