1. Quadratics Flashcards
What is the standard form a quadratic is given in?
What is the graph of the quadratic called?
Parabola - ‘u’ (if positive) or ‘n’ (if negative) shaped curve
How do you write a quadratic in completed square form?
The vertex of the quadratic will have the coordinates (h,k)
there is a change in sign on the ‘h’
EXAMPLE:
a) write y=x^2 + 6x + 10 in completed square form
b) sketch the quadratic
c) state the equation of the line of symmetry
If a question asks you to find the equation of a quadratic in standard form and gives you
a) the vertex
b) a specific point the quadratic passes through
What do you do?
Step 1: input given info into completed square form
Step 2: solve for “a”
Step 3: input “a” into initial CTS form and solve
E.g
What is the method when completing the square if the coefficient of x^2 is not 1?
What form must quadratics be before they can be solved?
How do you solve a quadratic by factorisation?
Step 1: start by using the form
(x ) (x ) = 0
Step 2: find two numbers that
a) multiply to give “c”
b) add to give “b”
* it is a process of trial and error (watch out for signs!)*
Step 3: solve by making the brackets equal to zero to find the values of x
Factorising:
Proof question ( ASK MISS HOW TO DO PROOF QUESTION ON PAGE 6 OF BOOKLET AND THEN ADD IT IN HERE)
What is the quadratic formula?
How do you solve a quadratic using the quadratic formula?
How do you find a quadratic when given the roots? (Quadratic formula)
How do you solve a disguised quadratic?
Why do we need to be careful when squaring the get final solutions when dealing with disguised quadratics?
Squaring can lead to introducing an incorrect solution - we must check by substituting answers back in to initial expression
E.g
What is the discriminant of:
How many solutions are there when the discriminant > 0
TWO solutions
How many solutions are there when
the discriminant = 0
ONE (repeated) solution
How many solutions are there when the discriminant < 0
None
How do you determine how many solutions a quadratic has using the discriminant
Step 1: input the values of a, b and c from the quadratic into the discriminant
Step 2: solve and use rules to determine how many solutions it has
Harder question using the discriminant example:
Modelling:
