Identify the transformations
f(x) = 2(x - 3)2
Vertical stretch by 2
Horizontal shift right three units
The parent quadratic function shift left 9 units and down 7
f(x) = (x + 9)2 - 7
Identify the vertex
f(x) = - 3(x + 6)2
(-6, 0)
(x + 3)(x - 9)
x2 - 6x - 27
p(x) = - x2 - 6
Reflection across the x - axis
Vertical shift down 6
f(x) = x2
Reflected across the x- axis, Vertical translated down 1 unit and vertically stretched by 5
f(x) = - 5x2 - 1
Find the solutions
p(x) = 3x2 + 15x + 18
x = - 2, and x = - 3
(5 + i)2
-25 + 10i
g(x) = 0.25(x - 6)2
Vertical compression
Horizontal shift right 6 units
f(x) = x2
Translated 9 units to the right, Shifted up 3 units
f(x) = (x - 9)2 + 3
Find the discriminant and the type of roots
f(x) = -2x2 - 10x + 20
d = 260 2 real roots
The high school choir hosts a concert for the community. The members of the choir sell tickets for the concert. Each member of the choir sells 3 tickets. Tickets are also sold at the door before the concert. A total of 125 tickets are sold at the door. How many total tickets are sold if there are 18 members of the choir?
175
All of the following transformations occur in
p(x) = 2(x + 7)2 + 5 EXCEPT
a. Reflection across x- axis
b. Shift up 5 units
c. Shift right 7 units
d. Vertical stretch by 2
A and C
Reflection across x- axis
Shift right 7 units
What values of a will result in a Vertical compression?
a. 5 c. - 3
b. - 1. 5 d. 0.25
d. 0.25
You have to design a drain using a sheet of metal that is 24 feet wide. Find the greatest possible cross-sectional area and the dimensions that allow the greatest possible area.
a = 72 ft2 h = 6 ft w = 12 ft
2x2(4x3 - 3x2 + 6x)
8x5 - 6x4 + 12x3
w(x) = - 2(x + 1)2 + 2
Reflection across x- axis
Vertical stretch by 2
Left one unit
Up 2 units
Write a function that has a horizontal shift right, Vertical shift down, reflection across the x- axis, and a vertical stretch
Answers will vary
You have to fence in a field using 400 feet of fencing. Find the greatest possible area of the field using the fencing.
100, 000 ft2
What are the order of operations?
Parenthesis Exponents Multiplication Division Addition Subtraction