Adaptive Perseverance: Students will persist in solving and graphing complex quadratic functions despite challenges, exploring multiple methods for accurate results.
Learner’s Mindset: Students will demonstrate curiosity and openness to learning different methods for solving quadratic equations and graphing functions.
Communication: Students will articulate their understanding of quadratic functions and their solutions clearly, both verbally and in writing.
Responsibility: Students will take responsibility for the accuracy and integrity of their solutions and graphs, ensuring they meet the required standards.
Global Citizenship: Students will understand the relevance of quadratic functions in real-world applications, recognizing their importance in various fields.
Critical Thinking: Students will analyze and evaluate different methods for solving quadratic equations and graphing functions, applying logical reasoning to interpret and write equations.
Collaboration: Students will work together to solve and graph quadratic functions, leveraging each other's strengths and perspectives for effective learning.
How do the different forms of a quadratic equation (standard, vertex, and factored) influence the graph of the function?
What are the steps and methods to find the roots of a quadratic function, and how do they compare in different scenarios?
How can we write a quadratic function given its graph and key features such as vertex, axis of symmetry, and roots?
Students will graph quadratic functions accurately and identify key features such as the vertex, axis of symmetry, and roots.
Students will use factoring, the quadratic formula, and completing the square to find the roots of quadratic functions, demonstrating their understanding through correct solutions.
Students will analyze graphs of quadratic functions to write corresponding equations, explaining their process and reasoning.
Students are able to convert quantitative problems that use words into mathematical expressions.
CCSS.MATH.CONTENT.HSF.IF.C.7.A: Graph quadratic functions and show intercepts, maxima, and minima.
CCSS.MATH.CONTENT.HSA.REI.B.4: Solve quadratic equations in one variable.
CCSS.MATH.CONTENT.HSA.SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
CCSS.MATH.CONTENT.HSF.BF.B.3: Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs.
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