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
Write the solution in interval notation:
x^2+2x-3<0
(-3,1)
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
Write the solution in interval notation:
x^2+2x-8>=0
(-oo,-4]uu[2,oo)
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
Write the solution in interval notation:
-x^2+x+2>=0
[-1,2]
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
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 x- and y-intercepts:
f(x)=12x^2+5x-3
x-int:
(-3/4,0), (1/3,0)
y-int:
(0,-3)