Math- Algebra 1 Core Map Quarter 3
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Quadratic Equations and the Quadratic Function Solving Quadratic Equations Graphically Solving Quadratic Equations by Completing the Square Quadratic Functions in Vertex Form Graphing Quadratic Functions Transformations of Quadratic Functions The Quadratic Formula and the discriminant Modeling with Quadratic Equations Solving Quadratic-Linear System of Equation Analyzing Functions with successive differences
Systems of quadratic and linear functions Find solutions to quadratic and linear functions graphically Solve systems of Quadratic and Linear Functions algebraically Prove solutions to Systems algebraically Applications of Systems of Quadratic and Linear Functions Graphically
Cubic Functions Graphing cubic functions Transforming cubic functions Solving cubic functions Connecting zeros, roots and solutions found algebraically to graph
Square Root Functions Graphing Square Root functions Transforming Square Root Functions Solving Square Root Equations Simplifyiing Radical Expressions Operations with Radical Expressions Solving Radical Equations
Function Features Increasing/Decreasing Positive/Negative Relative Max/Min Symmetries End Behavior Build New Functions
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Quarter 3 |
Quadratic Equations and Functions To solve quadratic equations, the polynomial should be listed in standard form Solving quadratic equations using: factoring, graphing, completing the square, and the quadratic formula. The roots, zeros and solutions to quadratics are found graphically on the x-axis Graphing quadratic equations-determining characteristics of the graph; vertex, axis of symmetry end behavior, domain and range Comparing transformed quadratics to the parent function Writing quadratic equations in vertex form Complete incomplete trinomials Use the discriminant to determine solutions Understand why the discriminant defines our solutions
Sytems of linear and quadratic equations Solutions to linear and quadratic systems are the points of intersection when the functions are graphed Solutions to linear and quadratic systems can be found algebraically using elimination and substitution. Solutions to linear and quadratic systems can be found using graphing calculator Solutions to linear and quadratic systems can be proven by showing solutions hold true in each function's equation.
Cubic Functions Graphing Cubic Functions-understanding the movement Domain and Range of Cubics Transformations of Cubic Functions Solving Cubic Equations and connecting the zeros, solutions or roots to the graphed function Determining if a point is on a given cubic function
Square Root Functions Squares of variables Square root function is an increasing function Characteristics of parent function Domain and Range of function Graph of Square root function Transformations of square root function Domain and Range of square root function Simplifying Radical Expressions Rationalizing the denominator Operations with radical expressions Simplifying nth root expressions Solving radical equations
Function Features Each function has specific end behavior There are domian intervals where the function is positive or negative Some functions have minimum or maximum values, others relative minima or maxima Some functions are symmetrical
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Quadratic Equations and Formulas Why and how does the graph of a quadratic equation differ from a linear function? What part of the function creates the symmetry that parabolas have? How can we find the line of symmetry of a graphed parabola? Is there more than one line of symmetry of the parabola? How do quadratic equations display themselves in real life? Why do quadratic equations have two roots? How can we use a graph to solve a quadratic equation? Is there a connection between the roots of the quadratic equation and the factors of the polynomials? Is there a way to predict the types of roots a quadratic might have? Can we determine the turning point and axes of symmetry of a parabola without graphing? Why is the vertex referred to as the turning point? How can we use our knowledge of perfect trinomials to complete the square and solve a quadratic? How was the quadratic equation developed and how can we use it to solve quadratic equations? What is the discriminant and what can we conclude from its value? How should we select the method to use to solve quadratic equations?
Systems of linear and quadratic equations What does a system of a linear and quadratic functions look like? At most, how many shared points can a quadratic and linear function share? What is the least amount of points, a quadratic and linear function share? Is there a way to determine these shared points algebraically? What does a graphed system with no solutions look like? How can you know that the solutions you determined, are in fact points on both lines? Can we determine the solutions using a graphing calculator?
Function Features How can we determine the end behavior of functions as they approach infinity or negative infinity? Can we determine domain intervals where a function is positive or negative? Do all functions have maximum and minimum points? Are all functions symmetrical? Can we build new functions from given functions?
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Quadratic Equations and Functions Write the quadratic equation in standard form Solve quadratic equations by factoring Using the zero product property to find the zeros and the roots Graphing the quadratic function (parabola) Determine the axis of symmetry on the graph Determine the axis of symmetry from a chart Determine the axis of symmetery using the formula Determine the maximum and minimum (vertex) Determine the domain and range of quadratic functions Translate the quadratic function Dilate the quadratic function Determine the transformations of a quadratic function from the vertex form of parabola Determine the vertex, from vertex form of a parabola Write a quadratic function in vertex form Determine the interval of the graph that is increasing or decreasing Examine end behavior of the quadratic function Determine the x and y intercepts graphically and algebraically Problem solving with quadratic functions Rate of change of a quadratic function Determine from a graph if there is one root, two distinct roots or no real roots Determine the roots by completing the square Finding the maximum or minimum using only algebra Solving using the quadratic formula Simplifying roots Analyzing successive differences - draw conclusions about the quadratic function
Systems of linear and quadratic systems Graph systems of linear and quadratic functions Determine the points of intersection are the solutions Prove the solution point is on both graphed functions Find the systems of linear and quadratic systems by using algebraic methods
Cubic Functions Graphing a cubic function from a table Graphing a cubic function from list using graphing calculator Transforming the cubic function Solving a cubic function by factoring Connecting the zeros, roots and solutions to the x-intercepts Determining if a point is on the give cubic function
Square Root Functions Graph the square root function Determine the domain and range of the parent function Determine the transformations of a square root function when compared to the parent Explain why the parent function has only domain values greater than zero Simplify Radical Expressions Rationalize the denominator Perform operations with radical expressions Solve square root equations Determine extraneous roots Function Features Determine end behavior Determine domain intervals where a function is increasing or decreasing Determine the maximum and minimum of a function Determine if a function is symmetrical Build a new function from a given function
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Quadratic Equations and Functions Quadratic functions standard form quadratic axis of symmetry vertex minimum maximum relative minima relative maxima double root translations transformation dilation vertex form completing the square quadratic formula discriminant successive differences parent function stretch shrink factors zero property roots zeros incomplete quadratic equations completed square radicand systems cubic root square root function radical function exraneous roots rationalize domain interval end behavior
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Pass the paper Pair share Exit Notes Classroom Assessments Writing prompt Dailly spiral review Weekly spiral review Benchmarks Self-Correcting Lab Assessment Algebra I Core Assessment STARS Assessment |
Algebra 1 - McGraw Hill Education Algebra 1- Amsco School Publications Big Ideas Algebra 1- Big Ideas Learning NYS Modules |
