Complex Numbers
Subtract:
(-2-6i)-(4-7i)
-6+i
2y^2=32
y=-4 or 4
x^2-2x-8=0
x=-2 or 4
A height of a model rocket t seconds after being launched is given by
h(t)=-16t^2+128t
How long is the rocket in the air?
The rocket is in the air for 8 seconds. (The height of the rocket is 0 feet for t = 0 and t = 8 seconds. This means the rocket is in the air 8 seconds before returning to the ground.)
Identify the axis of symmetry:
f(x)=3x^2-12x+5
x=2
Multiply:
6i(3+2i)
-12+18i
(x-2)^2=9
x=-1 or 5
y^2+11y+10=0
y=-10 or -1
A height of a model rocket t seconds after being launched is given by
h(t)=-16t^2+128t
What is the maximum height of the rocket?
Identify the y-intercept:
f(x)=(x+2)^2-3
(0, 1)
Simplify:
i^43
i^3=-i
4(y+5)^2=4
y = -6 or -4
x^2+2x-4=0
x=-1-sqrt5 or -1+sqrt5
MCC is creating a new rectangular parking lot. The length is 0.07 mile longer than the width and the area of the parking lot is 0.026 square mile. Find the length and width of the parking lot.
The width is 0.13 mile and the length is 0.2 mile.
x^2+0.07x-0.026=0
Identify the vertex:
f(x)=x^2-2x-3
(1, -4)
Multiply:
(2+i)(5-3i)
13-i
x^2+6x=7
x=-7 or 1
7x^2+4x-5=0
x=(-2-sqrt39)/7 or (-2+sqrt39)/7
The length of a rectangular poster is 1 ft more than the width. The diagonal of the poster is 5 ft. Find the length and width of the poster.
The length is 4 ft, the width is 3 ft
Identify the vertex:
y=2x^2-4x+5
(1,3)
Simplify:
(6i)/(3-i)
-3/5+9/5i
x^2+8x+25=0
x=-4-3i or -4+3i
2y^2=3y+4
y=(3-sqrt41)/4 or (3+sqrt41)/4
The daily profit P in dollars of the Pine Tree Table Company is given by the following function:
P(x)=-6x^2+312x-3672
How many tables are made per day if the company has a daily profit of zero dollars?
18 tables per day or 34 tables per day
Identify the x- and y-intercepts:
f(x)=12x^2+5x-3
x-int:
(-3/4,0), (1/3,0)
y-int:
(0,-3)