Radicals/Exponents
What is the product rule for exponents?
ax * ay=ax+y
What shift is being done?
y=x2+4
Vertical shift up 4
Factor:
6x2+23x+15
(6x+5)(x+3)
What is the standard form equation of a circle?
(x-h)2+(y-k)2=r2
Solve the following logarithm:
log525
2
What is the root, index, and radicand of the following radical expression?
cbroot(8)
root=2
index=3
radicand=8
Is this a vertical or horizontal shift?
y=(x+3)2
Horizontal shift 3 units to left
x2-6x+9
(x-3)(x-3)
or
(x-3)2
Find the center of the circle:
(x+1)2+(y-7)2=16
(-1,7)
What is the log of 1?
0
Solve the following expression.
(22)3
64
Reflection over the x or y axis?
y=-|x|
x-axis
Complete the square:
x2+6x+8=0
x=-2
x=-4
Steps:
x2+6x=-8
x2+6x+9=-8+9
(x+3)2=1
x+3=+/- 1
What is the radius of the following circle?
(x-256)2+y2=81
r=9
Expand the following logarithmic expression.
log2(x/x2)
log2x-2log2x
Solve the following radical using the product rule.
root(8) * root(2)
root(16)=4
Is this a compression or stretch?
y=-2x2+3
Stretch by factor of 2
Factor by grouping:
x3-2x2+5x-10
(x-2)(x2+5)
Graph this circle:
x2+(y-10)2=25
center: (0,10)
r=5
Convert the following logarithm to exponential form and solve.
log636=x
6x=36
x=2
What is the quotient rule for radicals?
root(a/b)=root(a)/root(b)
How many transformations are applied to the function?
y=-.5(x-12)3+6
4
reflection over the x-axis, compression by a factor of 1/2, horizontal shift 12 units to the right, and a vertical shift of 6 units up
Factor:
4x4+12x3+6x2+18x
2x[(x+3)(2x2+3)]
The third planet from the sun
What is Earth?
log2560=x
x=1