Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems.
Add and subtract polynomials of degree one and degree two.
Write linear inequalities in two variables given a table of values, a graph, and a verbal description.
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.
Write linear equations in two variables given a table of values, a graph, and a verbal description.
Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two.
Graph the solution set of linear inequalities in two variables on the coordinate plane.
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 exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems.
Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
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.
Determine the domain and range of quadratic functions and represent the domain and range using inequalities.
Write systems of two linear equations given a table of values, a graph, and a verbal description.
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.
Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.
Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
Solve systems of two linear equations with two variables for mathematical and real-world problems.
Determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities.
Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.
Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
Evaluate functions, expressed in function notation, given one or more elements in their domains.
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 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.
Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.
Solve linear inequalities 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 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.
Decide whether relations represented verbally, tabularly, graphically, and symbolically define a function.
Write and solve equations involving direct variation.
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.
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).
Multiply polynomials of degree one and degree two.
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