# 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)
- Quadratic Equation
- 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
- Quadratic Formula
- 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)
- Quadratic Functions
- 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