Updates
Bell Ringer What are the roots (solutions) of the graph of the quadratic equation? –1 and 3 –3 and 1 –1 and 1 1 and 3
Find the coordinates of the vertex of the graph of y = 4x2. Identify the vertex as a maximum or a minimum. (2, 0); maximum (0, 4); maximum (0, 4); minimum (2, 0); minimum
Which equation corresponds to the graph? y = x2  2x + 2 y = x2 + 2x + 2 y = x2 + 2x + 2 y = x2  2x + 2
Which graph corresponds with the equation y = (x  2)2  2?
Which quadratic function is equivalent to y = x2 + 2x  3? y = (x + 1)2  2 y = (x  1)2  4 y = (x  1)2  2 y = (x + 1)2  4
Review Lesson Complex Solutions
 Programming
 Axis of Symmetry
 Vertex
 Complex Solutions
 Brainstorming Activity
 Describe the difference between a parabola with a maximum and a parabola with a minimum value.
 Give examples of two different parabolas that have the same vertex.
 Explain how the axis of symmetry can help graph a quadratic function.
Exit Ticket Posted on board at end of block.
 Lesson Objective(s) How can the quadratic formula be used to solve problems?
Standard(s)  Graphing Quadratic Functions
 CC.912.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
 Solving Quadratic Equations
 CC.912.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable.
 CC.912.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.912.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
 CC.912.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.912.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
 CC.912.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.912.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.912.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.912.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.912.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.912.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.912.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.912.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real coefficients that have complex solutions.
 CC.912.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
 #4  Model with mathematics
 #5  Use appropriate tools strategically
 #7  Look for and make use of structure
Past Checkpoints Graphing Quadratic Functions
 page 528529
 A  #8
 B  #34
 C  #36
 D  #4143
 Solving Quadratic Equations by Graphing
 page 536538
 E  #16
 F  #18
 G  #20
 H  #40
 I  #50
 Solving Quadratic Equations by Completing the Square
 Quadratic Formula
 page 550551
 P  #8
 Q  #22
 R  #30
 S  #32
 T  #34
 U  #48
 V  #50
