Polynomials and transforming graphs. Flashcards
What does a discriminate of more than 0 mean?
Two real and distinct roots.
What is the discriminat?
The b² -4ac part of a quadratic equation.
What does a discriminate equal to 0 mean?
There are two repeated roots.
What does a discriminate of less than 0 mean?
No real solutions.
What is a factor of a polynomial ?
An algebraic expression that divides the polynomial and leaves no remainder.
If f(x) is the polynomial and p(x) is the root then what is the quotient?
F(x)÷P(x) = q(x)
What is the order of a polynomial?
The highest power of X.
The no. of turning points is always one less than the highest power.
How are axes intercept of a polynomial found?
Substitute 0 as Y and X. When Y is 0 each bracket should equal 0.
What is the factor therem?
If f(a) = 0 then x-a is a factor. The converse is also true.
What is the remainder theorem ?
If x-a isn’t a factor of F(x) then f(a) =r which is the remainder.
When 2x³ +3x² + kx-6 is divided by x+1 the remainder is 7. How would you go about finding K?
F(-1)=7.
Replace x with -1 to get an expression with a K in it. It should equal 7 and so solve.
K=-12
What do you do when a polynomial has 2 unknowns and two different remainders are given?
Calculate the two equations by using on remainder in each. Then add the two equations together to find one of unknows.
What would y=f(x-a)+b do to a graph of y=f(x)?
A translation of a units right, along the X axis and B units up along the Y axis.
What would writing an equation in complete the square form mean?
Re arrange it so it is X plus a value in squared bracket and add something to the side.
How would you transform a graph of y=x²-4 by 2 to the right?
It would by y=f(x-2) so where you have an x, it becomes x-2.
(X-2)²-4
