transformations and polynomials Flashcards
what are the dilations
from x and from y
reflections
from x and y
translations
vertical and horizontal
function for translations
y= Af(n(x-h) + R
affect y coordinates:
A- dilation from x and reflection from x
R- up/down
affect x coordinates:
n- dilation from y
h- left right
coordinate (3.4), 2 down, reflect in x, up 1, dilation of 2 from y
(3,2)
(3,-2)
(2,-2)
(4,-2)
what are the two ways of determining rules?
subbing of coordinates and solving and using elimination
how do you do a transformation using a matrix?
sub the numbers into the correct places, rearrange and then sub into the original equation
how are ways of factorising a quadratic?
cross method, inspection, complete the square, HCF, DOTs
how do you use TP from? how to find the TP
- CTS to get into that form
- sketch
- -b/2a
how do you complete the square?
halve, square, add, subtract the middle coefficient
put into squared brackets
how do you use long division?
divide leading coefficient into first, put answer up the top, multiple the answer by all of the terms and write those answers below with a subtraction
how do you use synthetic division and when can you use it?
take reciprocal of number from divisor and put it at the side. put the coefficients along the top, taking the first one to the bottom. multiply that number by the number out the front and then put it in the middle and subtract or add
can use it so long as the divisor is linear
remainder theorem
what can you use this for?
must must it equal to be a factor?
if P(a) = b then the remainder after dividing P(x) by (x-a) is b
- factorising
- 0
how do you sketch higher order polynomial which brackets?
multiply all of the x’s together to get the degree and charge
- the x ints are in the brackets
- multiply all numbers in the brackets to get the y int
how do you sketch a higher order polynomial without brackets
- positive/negative
- degree
- factorise for x ints
