Pure- Quadratics (2) Flashcards
How do you solve/ find the roots of a quadratic equation by factorising?
- Write in the form ax^2 +bx +c=0
- Factorise left-hand side
- Set each factor equal to zero and solve to find x
The quadratic formula
x=(-b +or- √(b^2-4ac))/2a
What is x^2+bx in completed square form?
(x+b/2)^2 - (b/2)^2
What is ax^2+bx+c in completed square form?
a(x+b/2a)^2 +(c-(b^2/4a))
What is a function?
A mathematical relationship which maps each value of a set of inputs to a single output
-written in form f()
What is the domain?
The set of possible inputs for a function
What is the range?
The set of possible outputs for a function
What are the roots of a function?
The values of x for which f(x)=0
How do you find the turning point of a quadratic graph?
- Complete the square
- If f(x)=a(x+p)^2 +q , y=f(x) has a turning point at (-p,q)
What is the discriminant?
For f(x)=ax^2 +bx+ c the discriminant is b^2-4ac. The value determines the number of roots f(x) has.
How many roots if the discriminant is >0?
2 distinct real roots
How many roots if the discriminant =0?
1 repeated real root
How many roots if the discriminant<0?
No real roots
