Quadratic Functions

Question 0

Types of quadratics

Answer 0

1) monic- coefficient of x^2 = 1

2) non monic- coefficient of x^2 is not 1

Question 1

Solving quad equations

Answer 1

1) factorisation
2) completing the square
3) quadratic formula

Question 2

Solving quad inequalities graphically

Answer 2

1) f(x)>0 ABOVE
2) f(x)=0 ON
3) f(x)<0 BELOW

Question 3

The discriminant

Question 4

1) if

Answer 4

• –> NO REAL ROOTS
  - > pos definite a>0
  - > neg definite a<0

Question 5

2) If

Answer 5

—> 2 EQUAL ROOTS

Question 6

3) if

Answer 6

• –> 2 UNEQUAL ROOTS

- > rational ->

Question 7

If ax^2+bx+c is congruent to Ax^2+Bx+C

Then:

Answer 7

A=a
B=b
C=c
*HINT
1) expand one expression then rearrange it in the form of the alternative expression
2) solve simultaneously

Question 8

Sum of roots where A and B are roots

Answer 8

A+B= -b/a

Question 9

Product of roots where A and B are roots

Answer 9

AB= c/a

Question 10

Roots special result where A and B are roots

Answer 10

A^2 + B^2 = (A+B)^2 -2AB

Question 11

The Discriminant and POIs

If we are asked to determine whether a quad function and an SLG have POIs, we must:

Answer 11

1) set up a simultaneous equation
2) rearrange the simultaneous equation so that we get a quadratic equation
3) using the quad equation, find