Quadratic Functions Flashcards
What is the general form of a quadratic?
ax^2 + bx + c = 0 or y
How to factorise when coefficienct of x is 1?
- Find two numbers that multiply to make c and add to make b.
- These are what go in the brackets.
The roots are whatever sum with these numbers to make the set of brackets 0.
What are the roots?
Where the curve crosses the x axis
How do you find the y intercept?
Factor in x = 0 into the original quadratic - y = ax^2 + bx + c. C is the y intercept
What is a perfect square - in terms of factorising?
When the quadratic factorised has only 1 repeated solution - (x +/- a)^2
How many times does the curve touch the x axis with a perfect square?
Once
What is the difference of 2 squares?
When bx = 0
What is the general form for the difference of 2 squares ?
a^2 -b^2 or (a-b)(a+b)
How do you factorise when the coefficient of x is not 1?
- Multiply a and c together.
- Find 2 factors of ac that sum to make b.
- Rewrite the quadratic with the 2 factors of ac that sum to make b/splitting bx.
- Split the quadratic into two parts - the first 2 terms as one part then the second two terms as the other.
- Individually factorise the two seperate parts.
- The terms on the outsides of the brackets make up one bracket, the terms on the inside of each bracket (which should be the same ) make up the second.
When the coefficient of x is negative what shape is the curve?
n shaped
How do you factorise a quadratic with a negative coeeficient of x?
- Factor out the negative.
- Factorise the quadratic as normal.
- Factor back in the negative - only for the first bracket.
What can you find by completing the square?
You can find the min and max points.
You can solve equations.
You can sketch curves.
You can find lines of symmetery.
When the coefficient of x is not 1 can you complete the square?
No
When the coeeficient of x is negative willl you find the minimum or max point?
The max
What is the general form for completeing the square ?
(x - p)^2 +/- q or
(x +/- b/2)^2 -(b/2)^2 +/- c
What is the vertex
The min or max point of a curve/the turning point.
How do you find the vertex
The x coor = whatever x is to make the completed square bracket sum to 0
The y coord = y is whatever is left after the bracket sums to 0
How do you find the line of sym?
Whatever the x coor is
What is the quadratic formula
-b +/- Root(b^2 - 4ac)/2a
Which part of the formula is the discriminant?
b^2 -4ac
When b^2 - 4ac > 0 how many solutions does the equation have?
2 Real distinct roots
When b^2 -4ac = 0 how many solutuions does the equation have?
1 real distinct repeated root
When b^2 -4ac < 0 how many solutions does the equation have?
None as when you sqr root the answer, it would give you an imaginary number.
What does the Root of a perfect square give us?
Rational roots
