Mystery Quadratics
Multiplying Polynomials
Gravity
Exponential Versus Quadratic
Visual Patterns
100
What number in the exponent signals that the expression is a quadratic?
2
100
x(x+1)
x2+x
100
What is the number that represents gravity?
16
100
Determine whether 5n2 or 3n will have greater value when: n=1
5n2
100
What function does this visual pattern represent?
Exponential, Linear, or Quadratic?
Linear
200
How many roots does a quadratic always have?
2
200
(x+2)(x-4)
x2-2x-8
200
Andre is standing on a beach, and throws a rock up in the air so that it will land in the air so that it will land in the ocean.
The graph shows the height of the rock, in feet, above the water as a function of time, in seconds.
How high above the water was the rock when Andre threw it? Explain how you know you know.
5 feet. At zero seconds the rock was at a height of 5 feet.
200
Determine whether 5n2 or 3n will have greater value when: n=5
3n
200
What function does this visual pattern represent?
Exponential, Linear, or Quadratic?
Quadratic
300
Which group of people was the first to study quadratics?
Babylonians, Greeks, or Chinese.
Babylonians
300
(x+2)2
x2+4x+4
300
Andre is standing on a beach, and throws a rock up in the air so that it will land in the air so that it will land in the ocean.
The graph shows the height of the rock, in feet, above the water as a function of time, in seconds.
When did the rock hit the maximum height? How high was it at its maximum height?
At 1 second the maximum height was around 21 feet.
300
x2 raced 2x
Which function is in the lead from 0<x<2.
2x
300
What function does this visual pattern represent?
Exponential, Linear, or Quadratic.
Exponential
400
What features about a function's graph signals it is quadratic.
Function is curved and shifts from either increasing to decreasing or vise versa.
400
(x-5)(x+5)
x2-25
400
Andre is standing on a beach, and throws a rock up in the air so that it will land in the air so that it will land in the ocean.
The graph shows the height of the rock, in feet, above the water as a function of time, in seconds.
Approximately, when did the rock hit the ocean?
The rock hit the ocean around 2.15 seconds.
400
x2 raced 2x
Which function is in the lead from 2<x<4.
X2
400
Here is a pattern of squares. S represents the number of small squares in the pattern as a function of n, the step number.
Which expression could define S?
C. n2+2
500
Why is it called quadratic?
The word "quadratic" comes from quadratum, the Latin word for square.
500
(2x+3)(x2-2x)
2x3-x2-6x
500
An orange is shot up into the air with a catapult.
The function h given by h(t) = 15 + 60t - 16t2 models the orange’s height, in feet, t seconds after it was launched.
Select all the true statements about the situation.
The domain of function h only contains values greater than or equal to 0.
The orange is the same height after 1 second after launch and 2 seconds after launch.
After 3 seconds, the orange hits the ground.
The orange is 15 feet above the ground when it is launched.
The value t = 10 does not belong in the domain of x.
Statements
1/4/5
500
x2 raced 2x
Which function wins the race to infinity?
2x
500
Here is a pattern of dots.
How many spots will be in step 10 and step n?
Step 10 : 101 dots
Step n:
f(n)=1+n2