quadratics

Question 1

when solving factorised quadratics consider the…

Answer 1

possibilities

Question 2

algebraic proof of minima and maxima

Answer 2

1. complete the square
2. write that (x+a)^2>0
   so (x+a)^2 +1>1
   therefore the quadratic will always be greater than 1

Question 3

how to complete the square

Answer 3

half the x coefficient and place this in a bracket with x. square the bracket. work out how much you would have to add or take away. combine this with the number on the outside.

Question 4

heading for graph sketch

Answer 4

shape, vertex, x ints, y ints

Question 5

intersection of quadratic with straight line

Answer 5

substitute to find point of intersection

Question 6

what is the discriminant

Answer 6

b squared minus four a c

Question 7

solve a quadratic inequality

Answer 7

find critical values
draw a graph
find what you need to

Question 8

if discriminant is less than zero

Answer 8

no real roots

Question 9

if discriminant equals zero

Answer 9

one real root, tangent

Question 10

if discriminant is greater than zero

Answer 10

2 real distinct roots

Question 11

what is the factor theorem

Answer 11

if f(x) is a polynomial and f(p)=0 then (x-p) is a factor of f(x)