Topic 4 Quadratic Functions

Question 1

For the curve y = a(x-h) square + k,
what are the four pieces of information that you need to know?

Answer 1

The shape of the curve depends on the value of a.

The coordinates of the turning point are (h,k) in this expression.

The maximum/minimum value of y is k and the corresponding value of x is h.

The equation of the line of symmetry is x =h.

Question 2

When a > 0, the graph has a ____________ point.

Answer 2

minimum

Question 3

When a< 0, the graph has a __________ point.

Answer 3

maximum

Question 4

For (x-a)(x-b)<0 where a<b, the solution is __________.

Answer 4

a<x<b

Question 5

For (x-a)(x-b)>0 where a<b, the solution is __________.

Answer 5

x<a>b</a>

Question 6

What is the solution set if you get this set form? {x : a< x < b}

Answer 6

(a,b)

Question 7

What is the solution set if you get this set form? {x:a (less than or equal symbol) x (lesser than or equal b)} ?

Answer 7

[a,b]

Question 8

What is the solution set if you get this set form? {x: a (less than or equal) x (less than) b}?

Answer 8

[a,b)

Question 9

What is the solution set if you get this set form? {x: a (less than) x (lesser than or equal to) b}?

Answer 9

(a,b]

Question 10

What is the solution set if you get this set form? {x: x < a }?

Answer 10

( -(infinity sign), a)

Question 11

What is the solution set if you get this set form? {x : x (bigger or equal to) b}?

Answer 11

[b, (infinity sign) )

Question 12

What is the solution set if you get this set form? {x: x (smaller than) a or x (bigger than) b}?

Answer 12

( -(infinity sign), a) union symbol (b, infinity sign)

Question 13

What is the solution set if you get this set form? {x: a (lesser than) x (lesser than or equal to) b and x (not equal) c } ?

Answer 13

(a, b] \ {c}

The dash stands for not including

C is an element —> when listing elements, we need to use curly brackets