Students will understand… A quadratic function has a parabolic shape. Quadratic equations can be solved in a variety of ways. Quadratic functions and equations can model real world phenomena. The key features of a quadratic function, expressed in a variety of ways, have contextual significance. There are relationships among the roots of an equation, the zeros of the corresponding function and the of the graph of the function. *RF1 Students will know … the general shape of a parabola the vertex, intercepts, domain & range and axis of symmetry the maximum and minimum values how to sketch/plot graphs how to identify the vertex of a quadratic from the standard form or graph identify the opening direction *RF2 Students will know … when to find the x-intercept or vertex x-intercepts are zeros and roots what solve means the difference between functions and equations how to use the quadratic formula when to solve an equation 8888 I*RF = Relations and Functions Skills: Enduring Understanding Specific Outcomes Description of Skills Students will understand… A quadratic function has a parabolic shape. Quadratic equations can be solved in a variety of ways. Quadratic functions and equations can model real world phenomena. The key features of a quadratic function, expressed in a variety of ways, have *RF1 Students will be able to… convert an equation from standard form to vertex form determine the vertex: from a graph from an equation in standard form using technology determine intercepts: from a graph from an equation in standard form using technology determine the domain & range from a graph sketch the graph of a quadratic function with or without technology determine the equation of the axis of symmetry intercepts
Level Excellent Proficient Adequate Limited Insufficient Criteria 4 3 2 1 Blank Math Content Scenario A All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given Math Content Scenario B All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given Math Content Scenario C All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given Presents Data Presentation of data is clear, precise and accurate Presentation of data is complete and Presentation of data is simplistic and plausible Presentation of data is vague and inaccurate Presentation of data is Explains Choices Provides insightful explanations Provides logical explanations Provides explanations that are complete but vague Provides explanations that are incomplete or confusing. No explanation is provided When work is judged to be limited or insufficient, the teacher makes decisions about appropriate intervention to help the student improve.
Public Awareness Campaign (continued) Role: You are to choose one of the following methods to support your public relations campaign. Audience You are to present to the mock parent group and convince them that quadratic functions and equations are a valuable asset to the Alberta Mathematics Curriculum. Product Your product should include: Four examples of parabolas in the real world. Include visuals. For one of your examples: Identify the vertex and its significance. Identify the y-intercept and its significance. Identify the number of x-intercepts and their significance. Determine the domain and range within the context of your example. Two quadratic equations in standard form: Calculate the x-intercepts using a minimum of two methods. Clearly show (or explain) all steps. Generate graphs of two quadratic functions, one in standard form and one in vertex form, using two of the following methods. table of values graphing calculator plot x-intercepts, y-intercept and vertex
minimum value - The least value of a dependent variable of a relation parabola – A U-shaped curve obtained by graphing a quadratic function quadratic equation – An equation of the form ax2 + b x + c = 0, where a, b, and c are real numbers and a ≠ 0 quadratic formula – The formula for determining the roots of a quadratic equation from its coefficients range - All possible dependent values for a relation root – A solution of an equation standard form – A quadratic function written in the form y = ax2 + bx + c, where a, b, and c are real numbers and a ≠ 0 vertex form – A quadratic function written in the form y = a (x - p)2 + q, where a, p, and q are real numbers and a ≠ 0 vertex of a parabola – The point of intersection of a parabola and its axis of symmetry x-intercept - The horizontal value of the point where the curve intersects the horizontal axis y-intercept - The vertical value of the point where the curve intersects the vertical axis. zero – The value of the independent variable of a function for which the function equals zero Other Appendix Copies of worksheets for Lessons 2 – 3 follow: Lesson 2 Investigate Vertex Form and Key Lesson 2 Jig Saw Applications and Key Lesson 2 Jig Saw Equation Forms and Key Lesson 2 Matching Activity with Key Lesson 3 Rectangles and Algebra Tiles Completion Assignment Lesson 3 Factoring Review Examples Lesson 3 Solving Using the Quadratic Formula Lesson 3 Solving Equations Questions and Key M20-2 Lesson 2 Investigate Vertex Form Investigate
Maximum or minimum value Minimum y = -9 y-intercept y = -8 x-intercept(s) x = -4, 2 Equation of the Axis of Symmetry x = -1 Domain Range Jig-Saw Problem - Stars Sketch a graph of the following quadratic function and complete the table provided. x y -5 477 -4 01 -1 -9 0 --8 0 2 0 3 77 Vertex (-1, -9)
Solve: . M20-2 Lesson 3 Solving Using the Quadratic Formula Key In General: The roots (solutions) of the quadratic equation can be found using the Quadratic Formula: Solve the quadratic equation using the quadratic formula. a = 1, b = 5, c = -14 x = -7, 2 Check 0 = 0 0 = 0 Solve the quadratic equation using the quadratic formula. a = 1, b = -2, c = -15 x = -3, 5 Check 0 = 0 0 = 0 Solve the quadratic equation using the quadratic formula. a = 2, b = 5, c = -12 x = -4, 3/2 Check 0 = 0 0 = 0
-7x2 - 21x = 0 x2 - 49 = 0 M20-2 Lesson 3 Solving Equations Questions Key Group 1 2, 4 1.5, 0.5 0, -5 +6, -6 Group 6 3, -5 -1, 2.5 0, 7 +3, -3 Group 2 3, -2 - 8, 0.25 0, 11 +2, -2 Group 7 -4, -8 3, -1.5 0, -9 +11, -11 Group 3 -6, 2 -3, 0.75 0, 2 +12, -12 Group 8 10, -18 2/3, 1 0, 7 +10, -10 Group 4 -7, 3 -4, 1.5 0, 5 +5, -5 Group 9 2, 1 1/3, 2 0, 2 +1, -1 Group 5 -1 -0.5, 6 0, -3 +7, -7