Key Features
Quadratic Forms
Standard to Factored/Vertex
Factored/Vertex to Standard
Other Stuff
100
How many key features are there?
14 total
x-intercept, x-intercept, y-intercept
Vertex, Axis of Symmetry, Increasing
Decreasing, Positive, Negative
Domain, Range, Left End Behavior
Right End Behavior, Opens
100
Name the 3 Quadratic Forms
Standard Form, Vertex Form, Factored Form
100
Switch the Standard Form to Factored Form:
y = x2 - 2x - 35
y = (x - 7)(x + 5)
100
Switch from Factored to Standard Form:
y = 5x2 - 5x - 10
100
A Sneaker Scientist is comparing Air Max Sneaker trends in the Winter Garden Nike Outlet for the years 2005-2020. The equation, y = 6(x - 8)2 + 192, represents the number of shoes sold, y, for each year since 2005, x.
- During what year were the least amount of Nike Air Max's sold?
- The Vertex is the LOW/MIN point: (8, 192)
x = years since 2005
In the year 2013 the store sold the lowest amount of Nike Air Max's.
200
When plotting the x-intercept points on a graph, what value is "0?"
y-value is always "0" for x-intercepts
200
Name the Form all the Key Features and their Values you can find from just this form:
y = -x2 - 2x + 8
Standard Form
1. y-int = (0,8)
2. Opens = Down
3. Left/Right End Behavior = y ---> - infinity
4. Domain = all real #s
200
Switch Standard to Vertex:
y = x2 - 2x - 35
y = (x - 1)2 - 36
200
Rewrite Factored to Standard Form:
y = 3(x + 2)(x - 7)
y = 3x2 - 15x -42
200
A Sneaker Scientist is comparing Air Max Sneaker trends in the Winter Garden Nike Outlet for the years 2005-2020. The equation, y = 6(x - 8)2 + 192, represents the number of shoes sold, y, for each year since 2005, x.
- What are the constraints for the Domain and Range?
Domain: 0 < x < 15
Range: 192 < y < 576
300
How do you determine which way the parabola opens?
The first number of each Quadratic Form, or the A-value. Positive opens up, Negative opens down
300
Name the Form and list the values of all the Key Features you can find without doing any math:
y = -(x + 4)(x - 2)
Factored Form:
1. x-intercepts: (-4, 0), (2, 0)
2. Opens = Down
3. Left/Right End Behavior = y ---> - infinity
4. Domain = all real #s
5. Positive: -4 < x < 2
6. Negative: x<-4 and x>2
300
Switch from Standard to Factored:
y = 3x2 - 15x -42
y = 3(x + 2)(x - 7)
300
Factored to Standard:
y = 3x2 +12x - 63
300
A Sneaker Scientist is comparing Air Max Sneaker trends in the Winter Garden Nike Outlet for the years 2005-2020. The equation, S(x) = 6(x - 8)2 + 192, represents the number of shoes sold, y, for each year since 2005, x.
- How many shoes were sold in 2015?
S(10) = 6(10 - 8)2 +192
y = 216
400
Which Key Feature is needed in order to provide the answers for Positive and Negative y-values
X-intercepts
400
You can find the y-intercept from which form or forms by setting the x-value to "0" and solving for which value?
All 3 forms, solve for the y-value
400
Standard to Vertex:
y = -4x2 +24 + 64
y = -4(x - 3)2 +100
400
Vertex to Standard:
y = -(x + 1)2 + 9
y = -x2 -2x + 8
400
A Real Estate Team just bought a 100 unit apartment building and plans to rent all of the apartments out. The function F(a) = -10a2 + 1760a - 50,000 represents the profit earned F(a), depending on the amount of apartments, a, they rent.
1. Rewrite the equation in Vertex form
y = -10(a - 88)2 + 27440
500
What 2 key features are need to provide the Range?
Vertex (y-value), and Opens (Up or Down)
500
Name the form, and list all the values of the key features that can be found:
y = -(x + 1)2 + 9
Vertex Form
1. Vertex: (-1, 9)
1. y-int = (0,8)
2. Opens = Down
3. Left/Right End Behavior = y ---> - infinity
4. Domain = all real #s
5. AOS: x = -1
6. Increasing: x<-1
7. Decreasing: x>-1
8. Range: y < 9
500
Switch from Standard to Both (Factored and Vertex):
y = x2 - 10x - 24
Factored: y = (x - 12)(x + 2)
Vertex: y = (x - 5)2 - 49
500
Switch from Vertex to Standard......then Standard to Factored:
Standard:
Factored:
y = 6(x-2)(x+4)
500
A Real Estate Team just bought a 100 unit apartment building and plans to rent all of the apartments out. The function F(a) = -10a2 + 1760a - 50,000 represents the profit earned F(a), depending on the amount of apartments, a, they rent.
1. What does the vertex coordinates mean in this context?
y = -10(a - 88)2 + 27440
