The Quadratic Formula and Graphs

The Quadratic Formula and Graphs Description A Year 11 lesson exploring how to solve quadratic equations that do not factorise easily using the quadratic formula, while connecting algebraic solutions to the features and shape of parabolas. Summary Students recap key quadratic vocabulary and the standard form ax² + bx + c = 0 before identifying the coefficients a, b and c. They practise substituting values into the quadratic formula, interpret the discriminant, and explore how the coefficient of x² affects the orientation of a graph. The lesson concludes with graph-sketching and application challenges. What you get Clear explanation of the quadratic formula Vocabulary practice covering key quadratic terms Retrieval questions on factorisation and standard form Step-by-step worked example Practice identifying a, b and c Explanation of the discriminant and its meaning Parabola anatomy: roots, vertex and y-intercept Comparison of positive and negative values of a Interactive ordering, true-or-false and fill-in-the-blank activities A final sketching challenge using a quadratic graph Content suitable for Year 11 students in England