Polynomials and Quadratics Flashcards
When a question says solve, what does it mean?
Find the values of x
How do you find the roots?
Set = 0
Factorise
Solve for x
How do you find roots if the equation can’t be factorised?
Set = 0
Sub into quadratic formula
Solve for x
What is the quadratic formula?
(-b +- v//b^2 - 4ac)/2a
What does (x+__)^2 mean?
It is a repeated root
What is the discriminant?
b^2 -4ac
If the discriminant > 0, what are the roots?
Real and distinct roots
If the discriminant = 0, what are the roots?
Real and equal roots
If the discriminant < 0, what are the roots?
No real roots
How do you determine the nature of the roots?
Make sure equation is in the form ax+bx+c=0
Sub equation into the discriminant
b^2 - 4ac <=> 0
statement
How do you complete the square?
Open brackets, put in ax^2 and bx, leave a space, close brackets, put c outside
Divide bx by 2 to get (1), square (1) to get (2)
Put (2) in the gap and take it away outside
Put into form (x+p)^2 +q
P = (1)
Q = c+(2)
What are the steps in sketching a parabola?
'Cuts y-axis when x=0' Find the nature of the roots through b^2 - 4ac 'Cuts x-axis when y=0' - factorise Find TP by completing the square Draw and label the graph
How do you extract the TP from (x+p)^2 + q
TP (-p,q)
How do you find the equation of parabola’s?
Extract roots (x values) from given co ordinates Roots : x = \_\_\_, x = \_\_\_\_ ((If x=1 then x-1=0)) y=k(x+\_\_)(x+\_\_)(x+\_\_) Sub the y-intersect into equation (e.g. (0,12)) 12=k(\_\_)(\_\_)(\_\_) Find k Sub k into the equation Break brackets Simplify
What is aimed to be achieved by a quadratic inequality?
Find the values that x can be