Jeopardy: Algebra 2 EOC Review

Answer Key

Linear Equations

Q: What is the slope-intercept form of a linear equation?

A: y = mx + b

Q: How do you find the x-intercept of a linear equation?

A: To find the x-intercept, set y = 0 and solve for x.

Q: What does the slope of a linear equation tell you about the graph?

A: A negative slope indicates a decreasing line; a positive slope indicates an increasing line.

Q: What is the process for evaluating a linear function?

A: Substituting a value of x into the equation to find the corresponding y value.

Q: What is the relationship between the slopes of parallel and perpendicular lines?

A: Parallel lines have the same slope, and perpendicular lines have slopes that are negative reciprocals.

Quadratic Functions

Q: What is the standard form of a quadratic function?

A: y = ax^2 + bx + c

Q: What is the vertex form of a quadratic function?

A: The vertex form is y = a(x - h)^2 + k.

Q: How do you find the axis of symmetry of a quadratic function?

A: The axis of symmetry can be found using the formula x = -b/(2a).

Q: What can you say about the vertex of a parabola based on its direction?

A: A parabola that opens upwards has a minimum point, and one that opens downwards has a maximum point.

Q: What role does the discriminant play in solving quadratic equations?

A: The discriminant (b^2 - 4ac) determines the number and type of roots of the quadratic equation.

Systems

Q: What does the solution to a system of linear equations represent?

A: The solution is where the lines intersect.

Q: What are two methods for solving systems of equations?

A: Substitution and elimination are two methods used to solve systems.

Q: What does it mean if the graphs of a system of equations are parallel?

A: If the lines are parallel, the system has no solution.

Q: What are the three possible outcomes when solving a system of equations?

A: A system can have one solution, no solution, or infinitely many solutions.

Q: Differentiate between consistent and inconsistent systems of equations.

A: Graphically, a consistent system has at least one intersection point, while an inconsistent system has no points of intersection.

Absolute Value

Q: What is the definition of absolute value?

A: The absolute value of a number is its distance from 0 on the number line.

Q: How do you solve an absolute value equation like |x| = a?

A: To solve an absolute value equation, set up two separate equations and solve each one.

Q: What does the graph of an absolute value function look like?

A: The graph of an absolute value function is a V-shape.

Q: How would you solve the inequality |x - 3| < 5?

A: The equation |x - 3| < 5 represents an interval; solve by recognizing the inequality.

Q: What are real-world applications of absolute value?

A: Absolute value can express distances, serving many practical purposes like measuring temperature differences.

Polynomials

Q: What is a polynomial?

A: A polynomial is an expression that consists of variables raised to whole-number exponents and coefficients.

Q: How do you determine the degree of a polynomial?

A: The degree is determined by the highest exponent in the polynomial.

Q: What does it mean to factor a polynomial?

A: Factoring polynomials involves writing them as a product of their factors.

Q: How do you find the roots of a quadratic polynomial?

A: The roots of a polynomial can be found using the quadratic formula when the degree is 2.

Q: What does the Rational Root Theorem state?

A: The Rational Root Theorem provides a way to identify possible rational roots of a polynomial.

Roots and Radicals

Q: What is a square root?

A: The square root of a number is a value that, when multiplied by itself, gives the original number.

Q: What constitutes a radical expression?

A: Radical expressions involve roots, such as square roots, cube roots, etc.

Q: What is the process for simplifying square roots?

A: To simplify a radical, look for perfect squares and factor them out of the radical.

Q: What does it mean to rationalize the denominator?

A: Rationalizing the denominator means eliminating the radical from the bottom of a fraction.

Q: How are the roots of a polynomial related to its coefficients?

A: The product of the roots of a polynomial can often be found using Vieta's formulas.

Functions

Q: What is the definition of a function?

A: A function is a relation where each input has exactly one output.

Q: What are the definitions of domain and range?

A: The domain includes all possible input values, while the range includes all possible output values.

Q: When is a function considered linear?

A: A function is linear if it can be expressed in the form y = mx + b.

Q: What is the vertical line test?

A: To determine if a relation is a function, use the vertical line test on its graph.

Q: What is a composite function?

A: Composite functions involve applying one function to the results of another; if f(x) = x + 2 and g(x) = 3x, find (f ∘ g)(x).

Exponents and Logarithms

Q: What do exponents represent?

A: Exponents denote repeated multiplication of a base number.

Q: How do logarithms relate to exponents?

A: Logarithms are the inverse operations of exponentiation.

Q: What is the product rule of logarithms?

A: The product rule for logarithms states logb(xy) = logb(x) + log_b(y).

Q: What is the power rule for exponents?

A: The power rule for exponents states that (x^m)^n = x^(m*n).

Q: What is the change of base formula?

A: The change of base formula allows you to convert logarithms to a different base: logb(a) = logk(a)/log_k(b).

Rational Functions

Q: What is a rational function?

A: A rational function is the ratio of two polynomials.

Q: What causes vertical asymptotes in a rational function?

A: The vertical asymptotes occur where the denominator is zero and not the numerator.

Q: How is the horizontal asymptote of a rational function determined?

A: The horizontal asymptote is determined by the degrees of the numerator and denominator.

Q: How do you find the zeros of a rational function?

A: To find the zeros of a rational function, set the numerator equal to zero and solve.

Q: What are holes in rational functions?

A: There can be holes in the graph where a factor cancels out in both the numerator and denominator.