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pure 1. Quadratics 4. Factorising, quadiratics ys ax* + be +0 when a= 1 (a, b and © are numbers ) ax* + bx +e x + te +120 (n+ Vrs )=0 Vie Isubhract 2 > (4) 2 numbers shat multiply == © C12) Gv +3 )Ue +4) 20 aen4 then a #4, you need more brain juice an’ tt + 6 +0 4o get +6 (x Ya -)s0 and “ay 8 wy ae —Gre a ae ok ned 2 2. Compeing, the Square. & for sketching graphs ; solving quadratic equations , circle equations ax*+bn +e —4 afri+b \i 4d the 2a / adjusting number divide by 2 rmullily out & adust equal original quadratic. (x46)* 5 —T/ (A) z+ ktn+ Gerd) 9 d= -20 —> = (1+6)"-20 & Sketch the Graph using the Completed Square. 220 260 [\- maximum point SS minimum point * quadrotics have 4 turning point grnereept a tuning point info (4, -1B) ye xt 14 + 36 : ‘G3 G) 13 factorise OK x-t+0 \ Y- coordinate. ear) the. square. 2+ t <— x- coordinate — — * y-int 8) Crt) fi a A 7 (0,36) — — roots | 2 - intercept (+480) 7 o) (4,713) 3. The quadlratic formula sR) (I _ discriminant 70 5 2 real rots a: _-b: bt Hae +0 > 4 real toot <0 5 no Lreal) roots how many roots ? ° Number of tools of a quadratic equation diseriminant: b*- Hac. ‘oe Uist eal 098 arab Tihewarve ls dhe fh a iH pon, € 0 two equal realrvas for epeaied alread) The curve totes the iso one point Ban nis Ta Tala The curve eliely Toco aay alow ean ofN\. woo : Tutersection of line and quod. curve. = _—— ‘two points of interscetion ‘one point of interseetion no points of intersection The line cuts the curve at two distinct points, line i The line touches the curve at cone point. This means that the a tangent to the curve ‘The line does not intersect the curve. two distinct real roots two distinet points of intersection ne point af intersection (line is 4 tangent) no real rools 0 0 two equitl real roots (repeated roots) 0 no points of interseetion 
