Podcast
Questions and Answers
What is the discriminant?
What is the discriminant?
b²-4ac
What is the discriminant when roots are equal?
What is the discriminant when roots are equal?
b²-4ac = 0
What is the discriminant when roots are imaginary?
What is the discriminant when roots are imaginary?
b²-4ac < 0
What is the discriminant when roots are rational?
What is the discriminant when roots are rational?
What is the discriminant when roots are irrational?
What is the discriminant when roots are irrational?
What is the sum of the roots of a quadratic?
What is the sum of the roots of a quadratic?
What is the product of the roots of a quadratic?
What is the product of the roots of a quadratic?
In absolute value, what does |x| < k imply?
In absolute value, what does |x| < k imply?
In absolute value, what does |x| > k imply?
In absolute value, what does |x| > k imply?
What is the solution for |x| = k?
What is the solution for |x| = k?
What is the general solution for x² + bx + c < 0?
What is the general solution for x² + bx + c < 0?
What is the general solution for x² + bx + c > 0?
What is the general solution for x² + bx + c > 0?
What are the steps to solve a radical equation?
What are the steps to solve a radical equation?
What does it mean when variables vary inversely?
What does it mean when variables vary inversely?
What does it mean when variables vary directly?
What does it mean when variables vary directly?
What is the equation for inverse variation?
What is the equation for inverse variation?
What is the equation for direct variation?
What is the equation for direct variation?
How do you evaluate f(g(x))?
How do you evaluate f(g(x))?
How do you convert degrees to radians?
How do you convert degrees to radians?
How do you convert radians to degrees?
How do you convert radians to degrees?
What is the compound interest formula?
What is the compound interest formula?
What is the continuous compound interest formula?
What is the continuous compound interest formula?
What is the center radius form of a circle?
What is the center radius form of a circle?
What is the variance?
What is the variance?
What is the distance formula?
What is the distance formula?
What is the sum of two perfect cubes formula?
What is the sum of two perfect cubes formula?
What is the difference of two perfect cubes formula?
What is the difference of two perfect cubes formula?
What is the difference of perfect squares formula?
What is the difference of perfect squares formula?
What is the value of i⁰?
What is the value of i⁰?
What is the value of i¹?
What is the value of i¹?
What is the value of i²?
What is the value of i²?
What is the value of i³?
What is the value of i³?
What is the value of i⁴?
What is the value of i⁴?
What is the conjugate of a + bi?
What is the conjugate of a + bi?
How do you rationalize a fraction with a monomial containing i in the denominator?
How do you rationalize a fraction with a monomial containing i in the denominator?
How do you rationalize a fraction with a binomial containing i in the denominator?
How do you rationalize a fraction with a binomial containing i in the denominator?
Given two roots of a quadratic, how do you write its equation?
Given two roots of a quadratic, how do you write its equation?
What is the period formula?
What is the period formula?
What is the frequency formula?
What is the frequency formula?
What is the x-coordinate of any point on a circle?
What is the x-coordinate of any point on a circle?
What is the y-coordinate of any point on a circle?
What is the y-coordinate of any point on a circle?
What is the sine ratio?
What is the sine ratio?
What is the cosine ratio?
What is the cosine ratio?
What is the tangent ratio?
What is the tangent ratio?
What is the secant ratio?
What is the secant ratio?
What is the cosecant ratio?
What is the cosecant ratio?
What is the cotangent ratio?
What is the cotangent ratio?
What are cofunctions?
What are cofunctions?
What does the acronym ASTC stand for?
What does the acronym ASTC stand for?
What is the quadratic formula?
What is the quadratic formula?
What is the log distribution rule for a product?
What is the log distribution rule for a product?
What is the log distribution rule for a quotient?
What is the log distribution rule for a quotient?
What is the log distribution rule for a power?
What is the log distribution rule for a power?
How do you convert log (base b) x = y to exponential form?
How do you convert log (base b) x = y to exponential form?
How do you convert b^y = x to log form?
How do you convert b^y = x to log form?
How do you determine the domain of a rational function?
How do you determine the domain of a rational function?
How do you determine the domain of a square root function?
How do you determine the domain of a square root function?
How do you determine the domain of a rational function with a square root in the denominator?
How do you determine the domain of a rational function with a square root in the denominator?
How do you determine the domain of a logarithmic function?
How do you determine the domain of a logarithmic function?
How do you find the inverse of a function?
How do you find the inverse of a function?
What does finding f(-x) do to f(x)?
What does finding f(-x) do to f(x)?
What does finding -f(x) do to f(x)?
What does finding -f(x) do to f(x)?
What happens when you compare f(x) + c to f(x)?
What happens when you compare f(x) + c to f(x)?
What happens when you compare f(x + c) to f(x)?
What happens when you compare f(x + c) to f(x)?
What is the axis of symmetry of a quadratic?
What is the axis of symmetry of a quadratic?
What is the multiplication of the same base (x^a)(x^b)?
What is the multiplication of the same base (x^a)(x^b)?
What is the division of the same base (x^a)/(x^b)?
What is the division of the same base (x^a)/(x^b)?
What is the power to a power (x^a)^b?
What is the power to a power (x^a)^b?
What is the negative exponent x^(-n)?
What is the negative exponent x^(-n)?
What is the rational exponent x^(a/b)?
What is the rational exponent x^(a/b)?
What is the exponential decay formula?
What is the exponential decay formula?
What is the exponential growth formula?
What is the exponential growth formula?
What is the magic number to complete the square?
What is the magic number to complete the square?
What is another word for multiplicative inverse?
What is another word for multiplicative inverse?
What is another word for additive inverse?
What is another word for additive inverse?
What is interval notation for x > a?
What is interval notation for x > a?
What is interval notation for x ≥ a?
What is interval notation for x ≥ a?
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.
