Quadratic Functions

Question 1

What is the general form of a quadratic?

Answer 1

ax^2 + bx + c = 0 or y

Question 2

How to factorise when coefficienct of x is 1?

Answer 2

1. Find two numbers that multiply to make c and add to make b.
2. These are what go in the brackets.
   The roots are whatever sum with these numbers to make the set of brackets 0.

Question 3

What are the roots?

Answer 3

Where the curve crosses the x axis

Question 4

How do you find the y intercept?

Answer 4

Factor in x = 0 into the original quadratic - y = ax^2 + bx + c. C is the y intercept

Question 5

What is a perfect square - in terms of factorising?

Answer 5

When the quadratic factorised has only 1 repeated solution - (x +/- a)^2

Question 6

How many times does the curve touch the x axis with a perfect square?

Answer 6

Once

Question 7

What is the difference of 2 squares?

Answer 7

When bx = 0

Question 8

What is the general form for the difference of 2 squares ?

Answer 8

a^2 -b^2 or (a-b)(a+b)

Question 9

How do you factorise when the coefficient of x is not 1?

Answer 9

1. Multiply a and c together.
2. Find 2 factors of ac that sum to make b.
3. Rewrite the quadratic with the 2 factors of ac that sum to make b/splitting bx.
4. Split the quadratic into two parts - the first 2 terms as one part then the second two terms as the other.
5. Individually factorise the two seperate parts.
6. 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.

Question 10

When the coefficient of x is negative what shape is the curve?

Answer 10

n shaped

Question 11

How do you factorise a quadratic with a negative coeeficient of x?

Answer 11

1. Factor out the negative.
2. Factorise the quadratic as normal.
3. Factor back in the negative - only for the first bracket.

Question 12

What can you find by completing the square?

Answer 12

You can find the min and max points.
You can solve equations.
You can sketch curves.
You can find lines of symmetery.

Question 13

When the coefficient of x is not 1 can you complete the square?

Answer 13

No

Question 14

When the coeeficient of x is negative willl you find the minimum or max point?

Answer 14

The max

Question 15

What is the general form for completeing the square ?

Answer 15

(x - p)^2 +/- q or

(x +/- b/2)^2 -(b/2)^2 +/- c

Question 16

What is the vertex

Answer 16

The min or max point of a curve/the turning point.

Question 17

How do you find the vertex

Answer 17

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

Question 18

How do you find the line of sym?

Answer 18

Whatever the x coor is

Question 19

What is the quadratic formula

Answer 19

-b +/- Root(b^2 - 4ac)/2a

Question 20

Which part of the formula is the discriminant?

Answer 20

b^2 -4ac

Question 21

When b^2 - 4ac > 0 how many solutions does the equation have?

Answer 21

2 Real distinct roots

Question 22

When b^2 -4ac = 0 how many solutuions does the equation have?

Answer 22

1 real distinct repeated root

Question 23

When b^2 -4ac < 0 how many solutions does the equation have?

Answer 23

None as when you sqr root the answer, it would give you an imaginary number.

Question 24

What does the Root of a perfect square give us?

Answer 24

Rational roots