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Questions
Bell Ringer
Review- Graphing Quadratic Functions
- How are key features of a graph of a quadratic function found?
- Graph quadratic functions.
- Recognize that a quadratic function has the shape of a parabola.
- Find the coordinates of the vertex of a parabola.
- Recognize whether the vertex of a parabola represents a minimum or a maximum.
- Find the equation of the axis of symmetry.
- Find the x and y-intercepts of a quadratic function.
- Forms of Quadratic Equations
- How can quadratic functions be represented to best describe the desired key features?
- Recognize standard form of a quadratic function.
- Recognize factored form of a quadratic function.
- Recognize vertex form of a quadratic function.
- Determine which forms of a quadratic function are best used for solve a problem.
- Completing the Square (video 1) (video 2)
- How can quadratic equations be solved using completing the square?
- Recognize perfect square quadratic equations.
- Create perfect square quadratic equations.
- Solve quadratic equations using completing the square.
- Quadratic Modeling
- How can quadratic equations be used to model real-world situations?
- Use key features of quadratic graphs to solve real-world problems.
- Connect real-world measurements to quadratic equations.
Lesson
Exit Ticket
- Posted on the board at the end of the block!
| Lesson Objective(s)
- Graph quadratic functions.
- Recognize that a quadratic function has the shape of a parabola.
- Find the coordinates of the vertex of a parabola.
- Recognize whether the vertex of a parabola represents a minimum or a maximum.
- Find the equation of the axis of symmetry.
- Find the x and y-intercepts of a quadratic function.
- Recognize standard form of a quadratic function.
- Recognize factored form of a quadratic function.
- Recognize vertex form of a quadratic function.
- Determine which forms of a quadratic function are best used for solve a problem.
- Recognize perfect square quadratic equations.
- Create perfect square quadratic equations.
- Solve quadratic equations using completing the square.
- Use key features of quadratic graphs to solve real-world problems.
- Connect real-world measurements to quadratic equations.
Standard(s)
- Graphing Quadratic Functions
- CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
- Solving Quadratic Equations
- CC.9-12.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable.
- CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
- Factored Form
- CC.9-12.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
- CC.9-12.F.IF.8a 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.
- Completing the Square
- CC.9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.
- CC.9-12.F.IF.8a 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.
- Quadratic Formula
- CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.
- Creating Quadratic Equations
- CC.9-12.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
- Comparing Quadratics Function with Different Representations
- CC.9-12.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
- Quadratic Modeling
- CC.9-12.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.
- CC.9-12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
- Complex Solutions of Quadratic Functions
- CC.9-12.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real coefficients that have complex solutions.
- CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Mathematical Practice(s)
- #1 - Make sense of problems and persevere in solving them
- #2 - Reason abstractly and quantitatively
- #7 - Look for and make use of structure
Past Checkpoints
- Graphing Quadratic Functions
- Solving Quadratic Equations by Graphing
- Form of Quadratic Equations
- Extra Practice
- Completing the Square (video 1) (video 2)
- Quadratic Modeling
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