Review of the topics studied in Grade 8
In Grade 8 you worked with the linear function y = kx + b and its graph, a straight line: k is the slope and b is the ordinate where the graph meets the Oy axis. A system of two equations in two unknowns is solved by addition or by substitution. For the quadratic equation ax² + bx + c = 0 the discriminant is D = b² − 4ac: if D > 0 there are two roots, if D = 0 one root, and if D < 0 there is no real root. For the reduced equation x² + px + q = 0, Vieta's theorem says x₁ + x₂ = −p and x₁ · x₂ = q. In a biquadratic equation ax⁴ + bx² + c = 0 we substitute t = x². We need all this in the new chapter on the quadratic function and quadratic inequalities.
“From roots to equation”: in pairs, one student thinks of two roots (for example 2 and −5), the other builds x² + px + q = 0 with Vieta's theorem, and then the first checks it with the discriminant.