Algebra 2 Trig Formulas Quiz

Questions and Answers

What is the discriminant?

b²-4ac

What is the discriminant when roots are equal?

b²-4ac = 0

What is the discriminant when roots are imaginary?

b²-4ac < 0

What is the discriminant when roots are rational?

b²-4ac is a positive perfect square Signup and view all the answers

What is the discriminant when roots are irrational?

b²-4ac is a positive non-perfect square Signup and view all the answers

What is the sum of the roots of a quadratic?

-b/a Signup and view all the answers

What is the product of the roots of a quadratic?

c/a Signup and view all the answers

In absolute value, what does |x| < k imply?

-k < x < k Signup and view all the answers

In absolute value, what does |x| > k imply?

x < -k OR x > k Signup and view all the answers

What is the solution for |x| = k?

x = k OR x = -k Signup and view all the answers

What is the general solution for x² + bx + c < 0?

r₁ < x < r₂ Signup and view all the answers

What is the general solution for x² + bx + c > 0?

x < r₁ OR x > r₂ Signup and view all the answers

What are the steps to solve a radical equation?

Isolate the radical, square both sides, solve the remaining equation Signup and view all the answers

What does it mean when variables vary inversely?

p₁q₁ = p₂q₂ Signup and view all the answers

What does it mean when variables vary directly?

p₁/q₁ = p₂/q₂ Signup and view all the answers

What is the equation for inverse variation?

xy = k Signup and view all the answers

What is the equation for direct variation?

x/y = k or y/x = k Signup and view all the answers

How do you evaluate f(g(x))?

Replace all of the inner function g into x of the outer function, f Signup and view all the answers

How do you convert degrees to radians?

Multiply by π/180 Signup and view all the answers

How do you convert radians to degrees?

Multiply by 180/π Signup and view all the answers

What is the compound interest formula?

A = P(1 + r/n)^(nt) Signup and view all the answers

What is the continuous compound interest formula?

A = P * e^(rt) Signup and view all the answers

What is the center radius form of a circle?

(x-h)² + (y-k)² = r² Signup and view all the answers

What is the variance?

(σx)² Signup and view all the answers

What is the distance formula?

Undefined Signup and view all the answers

What is the sum of two perfect cubes formula?

(a + b)(a² - ab + b²) Signup and view all the answers

What is the difference of two perfect cubes formula?

(a - b)(a² + ab + b²) Signup and view all the answers

What is the difference of perfect squares formula?

(a + b)(a - b) Signup and view all the answers

What is the value of i⁰?

1 Signup and view all the answers

What is the value of i¹?

i Signup and view all the answers

What is the value of i²?

-1 Signup and view all the answers

What is the value of i³?

-i Signup and view all the answers

What is the value of i⁴?

1 Signup and view all the answers

What is the conjugate of a + bi?

a - bi Signup and view all the answers

How do you rationalize a fraction with a monomial containing i in the denominator?

Multiply by i/i Signup and view all the answers

How do you rationalize a fraction with a binomial containing i in the denominator?

Multiply by the conjugate of the denominator Signup and view all the answers

Given two roots of a quadratic, how do you write its equation?

Determine the sum of the roots, set = -b/a. Determine the product of the roots, set = c/a. Replace into y=ax²+bx+c. Signup and view all the answers

What is the period formula?

2π/b Signup and view all the answers

What is the frequency formula?

2π/p Signup and view all the answers

What is the x-coordinate of any point on a circle?

x = r cos θ Signup and view all the answers

What is the y-coordinate of any point on a circle?

y = r sin θ Signup and view all the answers

What is the sine ratio?

sin θ = opposite leg / hypotenuse Signup and view all the answers

What is the cosine ratio?

cos θ = adjacent leg / hypotenuse Signup and view all the answers

What is the tangent ratio?

tan θ = opposite leg / adjacent leg Signup and view all the answers

What is the secant ratio?

sec θ = hypotenuse / adjacent leg Signup and view all the answers

What is the cosecant ratio?

csc θ = hypotenuse / opposite leg Signup and view all the answers

What is the cotangent ratio?

cot θ = adjacent leg / opposite leg Signup and view all the answers

What are cofunctions?

Two functions whose angles are complementary Signup and view all the answers

What does the acronym ASTC stand for?

All Students Take Calculus Signup and view all the answers

What is the quadratic formula?

Undefined Signup and view all the answers

What is the log distribution rule for a product?

log (XY) = log X + log Y Signup and view all the answers

What is the log distribution rule for a quotient?

log (X/Y) = log X - log Y Signup and view all the answers

What is the log distribution rule for a power?

log X^n = n log X Signup and view all the answers

How do you convert log (base b) x = y to exponential form?

b^y = x Signup and view all the answers

How do you convert b^y = x to log form?

log (base b) x = y Signup and view all the answers

How do you determine the domain of a rational function?

Set denominator ≠ 0 and solve. Signup and view all the answers

How do you determine the domain of a square root function?

Set radicand ≥ 0 and solve. Signup and view all the answers

How do you determine the domain of a rational function with a square root in the denominator?

Set radicand > 0 and solve. Signup and view all the answers

How do you determine the domain of a logarithmic function?

Set the argument > 0 and solve. Signup and view all the answers

How do you find the inverse of a function?

Switch x and y; get y alone. Signup and view all the answers

What does finding f(-x) do to f(x)?

Reflection in the y-axis Signup and view all the answers

What does finding -f(x) do to f(x)?

Reflection in the x-axis Signup and view all the answers

What happens when you compare f(x) + c to f(x)?

Moves f(x) c units in the vertical direction Signup and view all the answers

What happens when you compare f(x + c) to f(x)?

Moves f(x) c units in the horizontal direction Signup and view all the answers

What is the axis of symmetry of a quadratic?

x = -b / (2a) Signup and view all the answers

What is the multiplication of the same base (x^a)(x^b)?

x^(a+b) Signup and view all the answers

What is the division of the same base (x^a)/(x^b)?

x^(a-b) Signup and view all the answers

What is the power to a power (x^a)^b?

x^(ab) Signup and view all the answers

What is the negative exponent x^(-n)?

(1/x)^n Signup and view all the answers

What is the rational exponent x^(a/b)?

a√(b) Signup and view all the answers

What is the exponential decay formula?

y = a(1 - r)^t Signup and view all the answers

What is the exponential growth formula?

y = a(1 + r)^t Signup and view all the answers

What is the magic number to complete the square?

(b/2)² Signup and view all the answers

What is another word for multiplicative inverse?

reciprocal Signup and view all the answers

What is another word for additive inverse?

opposite Signup and view all the answers

What is interval notation for x > a?

(a, ∞) Signup and view all the answers

What is interval notation for x ≥ a?

[a, ∞) Signup and view all the answers

Study Notes

Quadratics

The discriminant formula is b² - 4ac.
Discriminant is zero (b² - 4ac = 0) when roots are equal.
For imaginary roots, the discriminant is less than zero (b² - 4ac < 0).
Positive perfect square discriminant indicates rational roots.
Positive non-perfect square discriminant indicates irrational roots.
Sum of roots of a quadratic: -b/a.
Product of roots of a quadratic: c/a.
Solutions for quadratic inequalities involve identifying roots and testing intervals.

Absolute Value

For |x| < k, the range is -k < x < k; for |x| ≤ k, it's -k ≤ x ≤ k.
For |x| > k, x is either less than -k or greater than k; for |x| ≥ k, include equalities.
Solving |x| = k gives x = k or x = -k; verify solutions.

Radicals

To solve radical equations, isolate the radical, square both sides, then solve.

Functions

Inverse variation: p₁q₁ = p₂q₂.
Direct variation: p₁/q₁ = p₂/q₂.
Inverse variation equation: xy = k (k is a constant).
Direct variation equation: x/y = k or y/x = k.
Function evaluation f(g(x)) involves substituting g(x) into f.

Trigonometry

Convert degrees to radians by multiplying by π/180; convert radians to degrees by multiplying by 180/π.
Period formula: 2π/b; frequency formula: 2π/p.
Coordinates on a circle: x = r cos θ; y = r sin θ.
Sine ratio: sin θ = opposite/hypotenuse.
Cosine ratio: cos θ = adjacent/hypotenuse.
Tangent ratio: tan θ = opposite/adjacent.
Reciprocal functions: sec θ = 1/cos θ, csc θ = 1/sin θ, cot θ = 1/tan θ.
Cofunctions are pairs of functions whose angles sum to 90°.
The acronym ASTC indicates which trig functions are positive in which quadrants.

Exponents

Interest compounded n times per year: A = P(1 + r/n)^(nt).
Interest compounded continuously: A = P * e^(rt).
Distance formula for points: d = √((x₂ - x₁)² + (y₂ - y₁)²).
Exponential decay: y = a(1 - r)ⁿ; exponential growth: y = a(1 + r)ⁿ.
For multiplication: (x^a)(x^b) = x^(a+b); for division: (x^a)/(x^b) = x^(a-b).
When raising a power to another power: (x^a)^b = x^(ab).
Negative exponents: x^(-n) = 1/(x^n).
Rational exponents: x^(a/b) = b√(x^a).

Statistics

Variance is represented as (σx)².

Logarithms

Logarithm product rule: log(XY) = log X + log Y.
Quotient rule: log(X/Y) = log X - log Y.
Power rule: log(X^n) = n log X.
Convert log(base b)x = y to exponential form: b^y = x.
Convert b^y = x to log form: log(base b)x = y.

Additional Concepts

Center-radius form of a circle: (x-h)² + (y-k)² = r².
Axis of symmetry for quadratics: x = -b/(2a).
Finding inverses involves switching x and y and solving for y.
Transformations: f(x + c) shifts horizontally, f(x) + c shifts vertically.

Complex Numbers

Powers of i: i⁰ = 1, i¹ = i, i² = -1, i³ = -i, i⁴ = 1.
Conjugate of a + bi is a - bi.
Rationalization involving i in the denominator uses its conjugate.

Functions and Intervals

Domain of rational functions determined by setting the denominator not equal to zero.
Domain of square root functions requires the radicand to be non-negative.
Logarithmic functions' domain found by ensuring the argument is positive.

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Description

Test your knowledge of key formulations related to quadratics in Algebra 2. This quiz covers the discriminant and its implications regarding the nature of roots. Perfect for reviewing concepts that may not be on your reference sheet.