Quadratics, Functions, Transformations, Geometry

Question 1

What is an quadratic equation

Answer 1

In the form ax2+bx+c=y

Question 2

What is a discriminant

Answer 2

b2-4ac determining root nature

Question 3

State the 3 root natures

Answer 3

b2-4ac=0 real and equal
b2-4ac>0 real and different
b2-4ac<0 no roots

Question 4

What is a function?

Answer 4

Rule that maps a single number to another single number

Question 5

What are domain and range?

Answer 5

Inputs for a function is domain

Set of outputs is range

Question 6

A function is inverse only if…

Answer 6

It is one one

Question 7

What is a one-one function

Answer 7

Distinct inputs have distinct outputs

Question 8

State the two opposite domain / range rules for f(x)

Answer 8

Domain of f = range of f-1

Domain of f-1= range of f

Question 9

How is graph of f-1(x) in relation to f(x)

Answer 9

F(x) is reflected in y=x

Question 10

f(x+a) is _ of _

Answer 10

Horizontal translation of -a

Question 11

f(x)+a

Answer 11

Vertical translation of +a

Question 12

f(ax) is _ of _ : _

Answer 12

Horizontal stretch of scale factor:1/a

multiply x coordinate by 1/a

Question 13

af(x) is _ of :

Answer 13

Vertical stretch of scale factor:a

multiply y coordinate by a

Question 14

What is gradient?

Answer 14

Measure of a straight lines slope with respect to it’s X axis

Question 15

State formula of gradient

Answer 15

(y2-y1/x2-x1)

Question 16

Formula of length a line joining 2 points

Answer 16

√(x1-x2)^2 + (y1-y2)^2

Question 17

State the rules of gradient for parallel and perpendicular lines

Answer 17

Para: equal
Perpen: product=-1

Question 18

Midpoint formula:

Answer 18

(x1+x2/2 , y1+y2/2)

Question 19

Equation of a line:

Answer 19

Y=mx+c

Question 20

Equation of a line with gradient m and passing through (x1, y1)

Answer 20

(y-y1) = m(x-x1)

Question 21

Equation of a line passing through 2 points

Answer 21

(y-y1) = (y2-y1/x2-x1)(x-x1)

Question 22

Equation of a circle with centre (a, b) and radius r

Answer 22

(x-a)^2 + (y-b)^2 = r^2

Question 23

x^2+y^2+2gx+2fy+c=0 represents?

Answer 23

A circle
Centre: (-g, -f) (that is /2)
Radius: √ g^2 + f^2 -c