Quadratics+in+Washington+State+Standards

Below are a list of Washington State Standards and Performance Expectations for this unit.



A1.1.A Select and justify functions and equations to model and solve problems. Students can analyze the rate of change of a function represented with a table or graph to determine if the function is linear. Students also analyze common ratios to determine if the function is exponential. After selecting a function to model a situation, students describe appropriate domain restrictions. They use the function to solve the problem and interpret the solution in the context of the original situation. A1.1.D Solve problems that can be represented by quadratic functions and equations. Examples: • Find the solutions to the simultaneous equations y = x + 2 and y = x2. • If you throw a ball straight up (with initial height of 4 feet) at 10 feet per second, how long will it take to fall back to the starting point? The function h(t) = -16t2 + v0t + h0 describes the height, h in feet, of an object after t seconds, with initial velocity v0 and initial height h0. A1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. • As constants such as a, b, and c in the equation y = ax2 + bx + c; A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A1.3.C Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x) = b.  A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. Example: • Kendre and Tyra built a tennis ball cannon that launches tennis balls straight up in the air at an initial velocity of 50 feet per second. The mouth of the cannon is 2 feet off the ground. The function h(t) = -16t2 + 50t + 2 describes the height, h, in feet, of the ball t seconds after the launch. Make a table from the function. Then use the table to sketch a graph of the height of the tennis ball as a function of time into the launch. Give a verbal description of the graph. How high was the ball after 1 second? When does it reach this height again? A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation. A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. Algebra 1 A1.8. Core Processes : Reasoning, problem solving, and communication Students formalize the development of reasoning in Algebra 1 as they use algebra and the properties of number systems to develop valid mathematical arguments, make and prove conjectures, and find counterexamples to refute false statements, using correct mathematical language, terms, and symbols in all situations. They extend the problem-solving practices developed in earlier grades and apply them to more challenging problems, including problems related to mathematical and applied situations. Students formalize a coherent problem-solving process in which they analyze the situation to determine the question(s) to be answered, synthesize given information, and identify implicit and explicit assumptions that have been made. They examine their solution(s) to determine reasonableness, accuracy, and meaning in the context of the original problem. The mathematical thinking, reasoning, and problemsolving processes students learn in high school mathematics can be used throughout their lives as they deal with a world in which an increasing amount of information is presented in quantitative ways and more and more occupations and fields of study rely on mathematics. Performance Expectations: Students are expected to: A1.8.A Analyze a problem situation and represent it mathematically. A1.8.B Select and apply strategies to solve problems. A1.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem. A1.8.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems. A1.8.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. A1.8.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose. <span style="background-attachment: initial; background-clip: initial; background-color: yellow; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial;">A1.8.G Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others. <span style="background-attachment: initial; background-clip: initial; background-color: yellow; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial;">A1.8.H Use inductive reasoning about algebra and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures.