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Identify and Graph Transformed Functions
(E) 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
A1.7.C(C) 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.
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Find Zeros of Quadratic Functions by Factoring
(7) Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.
A1.7.B(B) Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions
HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
HSF.IF.8.AHSF.IF.8.A Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
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Determine Whether a Relation is a Function
This Algebra 1 lesson teaches students how to whether a relation is a function. The lesson includes research-based strategies and strategic questions that prepare students for assessments. Students will identify the relation as a function if each domain value matches exactly one range value, and identify any ordered pairs that prevent the relation from being a function. Finally, they will interpret the solution. In addition to the lesson, there is one page of Independent Practice and three pages of periodic review.
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Determine the Domain and Range of a Relation Defined by a Graph
This Algebra 1 lesson teaches students how to determine the domain and range of the relation defined by the graph. The lesson includes research-based strategies and strategic questions that prepare students for assessments. Students will determine the domain by finding all x values defined by the graph, and they will determine the range by finding all y values defined by the graph. Then, they will interpret the answer. In addition to the lesson, there are two pages of Independent Practice and six pages of periodic review.
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Identify Key Points from Quadratic Function Graphs
(7) Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.
A1.7.A(A) 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
A1.7.B(B) Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions
A1.7.C(C) 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.
A1.8(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
A1.8.A(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula
HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
HSF.IF.8.AHSF.IF.8.A Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
HSF.IF.8.BHSF.IF.8.B Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing exponential growth or decay.
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Analyze Quadratic Function Forms
(B) 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)
A1.7.B(B) Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions
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Graph Piecewise Functions
(F) Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
PCAL.2.I(I) Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
QR.3.E(E) Determine or analyze an appropriate piecewise model for problem situations