Patterns
Determine the representation
From a graph
With a graphing calculator
Random
100
Write the Explicit Equation
x2
100
Determine if the following tables represent linear, quadratic, exponential, or neither and explain why. For any that are linear, quadratic or exponential, write the explicit formula.
Linear:
f(x)=-3x+1
100
Does this have a minimum or maximum?
Minimum
100
What two keys on your calculator at the most important for finding key features of a function?
Second
Calc/ Trace
100
a) 2x
200
What is the explicit equation?
x2+x
200
Determine if the following tables represent linear, quadratic, exponential, or neither and explain why. For any that are linear, quadratic or exponential, write the explicit formula.
Linear:
y=8x+3
200
(-1,0)
200
The graph represents a golf ball hit with an initial velocity of 8 meters per second from a platform 60 meters above ground on the Moon. The height of the ball after x seconds is given by the equation f(x)=60+8x-0.8x2
Find the value of f(10)
(10,60)
200
Describe how you can tell if a function is quadratic from:
a. An equation
b. A table
c. A graph
d. A diagram
Answers vary
300
What is the explicit equation?
2x2+2
300
Determine if the following tables represent linear, quadratic, exponential, or neither and explain why. For any that are linear, quadratic or exponential, write the explicit formula.
Quadratic:
x2+2
300
x=-1
300
The graph represents a golf ball hit with an initial velocity of 8 meters per second from a platform 60 meters above ground on the Moon. The height of the ball after x seconds is given by the equation f(x)=60+8x-0.8x2
Find the minimum/ maximum
(5,80)
300
Given: f(x)=3xand g(x)=3x2
1. Which function has the greatest average rate of change in the interval [1, 3]?
Same rate of change.
400
Write the explicit formula.
2x2+x-2
400
Exponential
f(x)=3x
400
What are the zero(s)
(-1,0)
400
The graph represents a golf ball hit with an initial velocity of 8 meters per second from a platform 60 meters above ground on the Moon. The height of the ball after x seconds is given by the equation f(x)=60+8x-0.8x2
Find the y-intercept and describe what it means in the context
(0,60) where the golf ball was originally hit.
400
Given: f(x)=3xand g(x)=3x2
Which function will have the greatest y-values for very large x-values?
f(x)
500
Draw a pattern to represent (x+2)2+1
Answers will vary
500
What would make a table neither?
Not a constant rate
Not a constant second difference
Not multiplied
500
Name the 4 key features of a quadratic
vertex (min/ max)
zeros
axis of symmetry
y-intercept
500
The graph represents a golf ball hit with an initial velocity of 8 meters per second from a platform 60 meters above ground on the Moon. The height of the ball after x seconds is given by the equation f(x)=60+8x-0.8x2
Find the domain and range
[0,15]
[0,80]
500
The term parabola comes from which famous Greek Mathematician?
The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve, as Apollonius had proved. The focus–directrix property of the parabola and other conic sections is due to Pappus.