IA1 / IA2
Graph: y = x + 4
See graph
Factor: y = x2 - 7x + 10
(x -5) (x -2)
Multiply: (3x - 3) (x + 5). What are a, b, and c?
a = ?
b = ?
c = ?
a = 3
b = 12
c = -15
f(x) = x2 - 6
g(x) = 3x - 1
What is f(2). What is g(2)?
f(2) = -2
g(2) = 5
Why are the following set of points not representative of a function?
(3,1)
(2,8)
(-1,7)
(3,4)
(-5,-11)
There is an x-value (x = 3) that repeats more than once. There are two different point where x = 3 meaning it is not a function and does not pass the Vertical Line Test.
Graph: y = -1/3x
See graph
Solve: x2 - 7x + 10
x = 5
x = 2
Multiply: (4x - 2)(4x + 2)(5x)
80x3 - 20x
f(x) = x2 - 6
g(x) = 3x - 1
For what value is f(x) > g(x)
a) 2
b) 3
c) 4
d) 5
Answer: D (x = 5)
f(5) = 19
g(5) = 14
The function x8 - y8 represents a special case of a quadratic function. What is the name of that special case function?
(Hint: Use your Resources on Special Case Quadratics)
Difference of Squares
What is the point of intersection of...
y = x + 4
and
y = -1/3x
(-3,1)
x = -3
y = 1
Which of the following is a step in completing the square for x2 - 5x + 1 = 0
a) (x - 5/2)2 = 21/4
b) (x + 5/2)2 = 21/4
c) (x - 5/2)2 = -21/4
d) (x + 5/2)2 = -21/4
a) (x - 5/2)2 = 21/4
Find the vertex of each quadratic equation below.
f(x) = x2 + 4x + 11
g(x): (4,20), (7,18), (10,16), (13,18)
Which vertex has the greater y-value?
Answer:
f(x) = (-2, 7)
g(x) = (10,16)
g(x) has the greater y-value.
State whether the following are rational or irrational...
1: 9 / (√9)
2: 9 + √11
1: RATIONAL
2: IRRATIONAL
Solve and plot on a number line:
(-5/3)x + 12 < -3x + 8
x < -3
See number line
f(x) = 11/4x + 65
The revenue John gains from bus tickets is represented by the function...
r(x) = 6x
How many bus tickets does John have to sell to break even?
11/4x + 65 = 6x
x = 20 tickets
What is the maximum height, in feet, of a projectile represented by the function:
f(x) = -15x2 + 60x + 90
150 feet
Solve for x:
(3x + 2)2 - (7x + 2) = 8x2 - 4x + 12
x = -10
x = 1
The cost of a Jordans sneaker membership is represented by the equation f(x) = -8,000x2 + 20,000x + 2,000, where f(x) is the cost in dollars and x is the number of Jordans.
Part A: Which of the following represents the domain of the function?
A) The domain is the set of all real numbers
B) The domain is the set of all negative numbers
C) The domain is the set of all integers
D) The domain is the set of all whole numbers
D) The domain is the set of all whole numbers
(# of shoes cannot be negative)
(# of shoes cannot be a fraction)
(# of shoes can be zero)
A pool has a length that is 6 feet longer than the width. Write an expression to represent the area of the pool.
The entire pool is then surrounded by a 2.5-foot walkway. Write a new expression for the area of the pool and walkway.
Original Expression: (x)(x + 6)
New Expression: (x + 5) (x + 11)
Graph: 14y - 28x = 56
Identify the x and y-intercepts of the graph
See graph
x-intercept: (-2,0)
y-intercept: (0,4)
Solve by completing the square:
x2 - 6x - 16 = 0
[Must have solved with completing the square, not factoring]
x = -2
x = 8
Graph: y = (x - 3)2 - 4
See graph
Vertex: (3,-4)
X-Intercepts: (1,0) and (5,0)
Y-Intercept: (0,5)
Two points on the graph of f(x) are...
(-2,1) and (3,4)
Write an equation for the line f(x)?
f(x) = 3/5x + 11/5
A pool has a length that is 6 feet longer than the width. The entire pool is then surrounded by a 2.5-foot walkway. If the area of the pool and walkway combined is 112 feet2, what are the original length and width?
Original Length: 9 feet
Original Width: 3 feet