# Algebra II Honors Final

## Terms

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Cube of a Binomial (-)
(u - v)³ = u³ - 3u²v + 3uv² + v³
Difference of Two Cubes
u³ - v³ = (u - v)(u² + uv + v²)
ax² + bx + c = 0
Standard Equation of an Ellipse
(x²/a²) + (y²/b²) = 1 ; (x²/b²) + (y²/a²) = 1
Volume of a Cube
V = s³
Standard Equation of a Hyperbola
(x²/a²) - (y²/b²) = 1; (x²/b²) - (y²/a²) = 1
Difference of Two Squares
u² - v² = (u + v)(u - v)
Test for Odd Function
f(-x) = -f(x)
Extracting Square Roots
The equation u² = d, u = ±√(d)
Asymptotes of a Hyperbola
y = .(b/a)x and; y = -(b/a)x or y = (a/b)x and y = -(a/b)x
Perimeter of a Square
P = 4s
Percent of Monthly Expenses
Monthly Expenses = Percent × Income
x = -b ± √(b² - 4ac)/2a
Point-Slope Form of the Equation of a Line
y - y₁ = m(x - x₁)
Circle
(x - h)² + (y - k)² = r²
Difference of Functions
(f - g)(x) = f(x) - g(x)
Simple Interest
Interest = principle × annual interest rate × time in years
The Fundamental Theroem of Algebra
If f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the complex number system
Cube of a Binomial (+)
(u + v)³ = u³ + 3u²v + 3uv² + v³
Perimeter of a Rectangle
P = 2l + 2w
Distance Problem
Distance = Rate + Time
Area of a Triangle
A = (1/2)bh
Rational Zero Test
Rational zero = (a factor of the constant term a₀)/( a facetor of the leading coefficient asubn)
Volume of a Rectangular Solid
V = lwh
Quotient of Functions
(f/g)(x) = f(x)/g(x), g(x) ≠ 0
Slope-Intercept Form
y = mx + b
Standard Form of a Quadratic Function
f(x) - a(x - h)² + k, a ≠ 0
Sum of Functions
(f + g)(x) = f(x) + g(x)
Continuous Compounding
A = Pe^rt
Square of Binomial (-)
(u - v)² = u² - 2uv + v²
Temperature
F = 9/5C + 32
Definition of Composition of Two Functions
( f ⁰ g)(x) = f(g(x))
Pythagorean Theorem
a² + b² = c²
Horizontal Line
y = b
Principal Square Root of a Negative Number
√(-a) = √(ai)
Product of Functions
(fg)(x) = f(x) × g(x)
Area of a Rectangle
A = lw
Midpoint Theorem
m = (x₁ + x₂)/2, (y₁ + y₂)/2
Compound Interest
A = P([1 + (r/n)]^nt
Sum of Two Cubes
u³ + v³ = (u + v)(u² - uv + v²)
Test for Even Function
f(-x) = f(x)
f(x) = ax² + bx + c
Area of a Sqare
A = s²
Square of a Binomial (+)
(u + v)² = u² + 2uv + v²
Volume of a Circular Cyloander
V = πr²h
Distance
distance traveled = rate × time
Area of a Circle
A = PI(r)²
Similar Triangles
(Height of A)/(Length of A's shadow) = (Height of B)/(Length of B's shadow"
Circumference of a Circle
C - 2πr
Hyperbola
a hyperbola is the set of all points (x,y) in a plane the difference of whose distances from the two distinct fixed points (foci) is a positive constant
The Equation of a Circle
(x - h)² + (y - k)² = r²
Distance from center of Circle
r = √[(x - h)² + (y - k)²]
Perimeter of a Triangle
P = a + b + c
General form of the equation of a line
Ax + By + C = 0
Slope of a Line Passing Through Two Points
m = (y₂ - y₁)/(x₂ - x₁)
Exponential Function
f(x) = a^x
Absolute Value Inequality
|x| < a iff -a < x a iff x < -a or x > a
Zeros of a Function
the x-values for which f(x) = 0
Volume of a Sphere
V = (4/3)πr³
Compound Interest
Balance = principle[interest + (annual interest rate/ compounding per year)]^(compounding per year × time in years)
Vertical Line
x = a
Linear Equation
ax + b = 0
Distance Formula
d = √[( x₂ - x₁) + (y₂ - y₁)]
Equation of Profit
Profit = Revenue = Cost
Ellipse
an ellipse is a set of all points (x,y) in a plane the sum of whose distances from two distinct fixed points (foci) is constant
Completing the Square
For the equation 1x² + bx = -c, add (b/2)² to each side, then factor
Percent of a Raise
Raise - Percent × Old Wage

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