10 ACM

Discriminant

100

Formula

b^2 - 4ac 

200

What do we use it for?

determine the number of solutions 

300

Determine the number of solutions for 

y=3x^2 + 6x - 3

2 solutions

400

one root means?

one solution

500

For the equations determine the value(s) of m which there are two real roots 

y = mx^2  − 6x + 9 

when m < 1

Circles

100

What is the translated equation of a circle 

(x-h)^2 + (y-k)^2 =r^2 

200

centre = (?, ?)

(h,k)

300

Domain and Range in Set Notation 

(x-1)^2 + (y+2)^2 =4 

Domain = [-1, 3]

Range = [0,-4]

400

determine radius 

(x-3)^2 + (x+1)^2 = 3

root 3 

500

(x-2)^2 + (y+3)^2 = 9 Find the end points

(2, 0) (2, -6) (-1, -3) (5, -3)

Quadratics

100

what is the TP ?

y=2(x-3)^2 +4 

(3, 4)

200

what 5 things do you need to include to sketch 

1. y-intercept 

2. x-intercept/s

3. Tp 

4. axis of symmetry

5. Nature 

300

Solve by Factorising

2x^2 +7x+3=0

x=-0.5 and x=-3

400

A farmer wants to create an enclosed rectangular area against the river bank. Determine the maximum area the farmer could make if they have 100m of fencing and don’t need to fence the river bank.

1250m^2 

500

A parabola has turning point (2, -1) and passes through the point (0,7). Determine the equation for the parabola. 

y=2(x-2)^2 -1 

Polynomials

100

P(x)=3x^2 + 2x -1

Find P(-1) 

0

200

Determine all solutions 

y=(x-1)(x+4) 

x=1 and x=-4

300

Determine all solutions 

y=(x-2)(x-3)(2x+4)

x=2, x=3 and x=-2 

400

Expand and simplify (x+1)(x-2)(x+2) 

x^3 +x^2 -4x -4

500

Expand and simplify 

(x+1)^4

x^4 + 4x^3 +6x^2 +4x +1