Simplify numerical radical expressions involving square roots.
Write systems of two linear equations given a table of values, a graph, and a verbal description.
Graph the solution set of linear inequalities in two variables on the coordinate plane.
Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
Determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities.
Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems.
Compare and contrast association and causation in real-world problems.
Write quadratic functions when given real solutions and graphs of their related equations.
Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems.
Add and subtract polynomials of degree one and degree two.
Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.
Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay.
Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1).
Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two.
Solve systems of two linear equations with two variables for mathematical and real-world problems.
Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.
Determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities.
Identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes.
Write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points.
Write linear inequalities in two variables given a table of values, a graph, and a verbal description.
Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems.
Write and solve equations involving direct variation.
Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.
Determine the domain and range of quadratic functions and represent the domain and range using inequalities.
Interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems.
Write linear equations in two variables given a table of values, a graph, and a verbal description.
Write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined.
Decide whether relations represented verbally, tabularly, graphically, and symbolically define a function.
Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax2+ bx + c).
Determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
Evaluate functions, expressed in function notation, given one or more elements in their domains.
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