polynomials & quadratics

Question 1

possible questions

Answer 1

• synthetic division
• find equation from graph
• discriminant
• complete the square
• solve quadratic inequalities
• relationship between line and parabola

Question 2

how do you find the factor if its not given in synthetic division?

Answer 2

trial and error of the factors of ax²+bx+c

Question 3

find equation from graph process

Answer 3

f(x)= k (x+a) (x+b) (x+c)
f(x)= k (x+2) (x-1) (x-3)
3= k (0+2) (0-1) (0-3)
3= k x(2) x(-1) x(-3)
3= 6k
k= 3/6
k= 1/2

Question 4

solve quadratic inequalities process

Answer 4

• roots (from factorising)
• sketch graph
• solution (e.g 1<x<5)

Question 5

find relationship between line and parabola process

Answer 5

• equal to 0 and simplify to ax²+bx+c=0
• find discriminant
• interpret discriminant b²-4ac (=0 or >0 or <0)
• factorise and find points of contact