3 - quadratics

Question 1

4 ways in which we can solve quadratics

Answer 1

• factorising
• completing the square
• approximating using a graph
• using the quadratic formula

Question 2

quadratic formula

Answer 2

x = (-b +- root b2-4ac) / 2a

Question 3

3 features needed in a sketch

Answer 3

• roots
• general shape - smiley face/hill
• y intercept

Question 4

turning point

Answer 4

y = (x+a)2 +b
min/max (-a,b)

Question 5

quadratic inequalities

Answer 5

• factorise
• draw graph - to see which bit is needed (<0 or >0)

Question 6

inequality set notation

Answer 6

{x: x<5} U {x:x>3}
{x: 5<x<7}

Question 7

discriminant

Answer 7

b2- 4ac
if >0 - 2 solutions
if = 0 - 1 solution
if <0 - no real solutions

Question 8

disguised quadratics

Answer 8

eg x^2/3 +2x^1/3 +2 = 0
just make y + x^1/2
and it becomes y^2 +2y +2 = 0
which you can solve