Algebra 2 Semester 1 Review

Review Problems

Algebra 2 Semester 1 Review covers various topics, including graphing transformations, writing equations of functions, and solving systems of equations.
Several problems involve finding the equation of a transformed function, given the graph of the original function.
Problem 1: Finding the function that represents the dotted graph, given the graph of y = f(x).
Problem type 1: Transformations of graphs.
Problem 2: Writing the equation of a function g(x) that shifts f(x) right 1 unit, given the graph of f(x) = |x|.
Problem 3: Finding the equation of a function g(x) which shifts f(x) = -2x² right 6 units.
Problem 4: Finding the equation of the graph that represents the dotted graph, given the graph of y = f(x). (Transformations involving shifts and reflections are likely involved).
Problem 5: Writing the equation of a function g(x) that shifts f(x) = 2|x| 4 units left and 6 units down.
Problem 6: Finding the function that describes the dotted graph, given the graph of y = x².
Problem 7: Solving a system of equations for three variables, likely using substitution or elimination methods.
Problem 8: Finding the difference of two given matrices, A - B.
Types of problems: Matrix operations, Solving systems of equations.
Problem 9: Finding the difference of the two matrices A - B.
Problem 10: Finding the difference of two given matrices A - B.
Problem 11: Solving a system of inequalities graphically.
Problem 12: Interpreting a graph relating chirps per minute to temperature.
Problem 13: Determining an equation and interpreting the y-intercept of a graph representing a salesperson's pay.
Problem 14: Finding the axis of symmetry from a given graph.
Problem 15: Finding the vertex of a parabola from a given graph.
Problem 16: Graphing a quadratic equation, finding the roots and the vertex.
Problem 17: Graphing a quadratic equation, finding the roots, vertex, and axis of symmetry (likely using completing the square or factoring).
Problem 18: Graphing a quadratic equation, finding the roots (likely using the quadratic formula).
Problem 19: Determining if a quadratic function has a minimum or maximum and finding the minimum/maximum value.
Problem 20: Solving a word problem involving the height of a rocket using a quadratic equation (likely finding the time when the height is zero).
Problem 21: Interpreting a graph depicting the height of a rocket over time. Determining time intervals where height is increasing or decreasing.
Problem 22: Determining the time a football is in the air, given a graph of its height over time.
Problem 23: Identifying maximum height of a toy rocket from a graph.
Problem 24: Calculating y-intercept from a quadratic equation in factored form.
Problem 25: Recognizing a given parabola's equation.
Problem 26: Writing a quadratic equation in standard form.
Problem 27 & 28: Solving quadratic equations by factoring.
Problem 29 & 30: Solving quadratic equations (likely using factoring, completing the square, or quadratic formula).
Problem 31 & 32: Solving quadratic equations using completing the square.
Problem 33: Identifying equations that have the same solution as a given quadratic equation.
Problem 34: Calculating the discriminant of a quadratic.
Problem 35: Solving a quadratic equation using the quadratic formula.
Problem 36 & 37: Solving quadratic equations for real solutions.
Problem 38: Finding the roots of a quadratic equation, expressed in a + bi form.
Problem 39: Evaluating a complex number expression.
Problem 40: Simplifying a square root expression.
Problem 41 & 42: Simplifying expressions that involve complex numbers.
Problem 43: Combining and simplifying polynomial expressions.
Problem 44: Expanding a binomial multiplication into a trinomial form.
Problem 45 & 46: Expanding and simplifying polynomial expressions.
Problem 47: Expanding and simplifying polynomial expressions in standard form.
Problem 48: Simplifying a rational expression involving a quadratic over a number.
Problem 49 & 50: Finding results of polynomial division (long division).
Problem 51: Using synthetic division to find remainders in polynomial division.
Problem 52: Finding a polynomial expression by knowing its quotient and remainder and divisor.
Problem 53: Interpreting a function representing an object's height over time.
Problem 54: Finding the range of a quadratic function through graphing.
Problem 55: Finding the range of an absolute value function.