Lesson 1: 2.1 Quadratic Functions

How do you sketch graphs and write equations of parabolas?

quadratic function, parabola, vertex, standard form

HSA-REI.B.4.a: 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.  
HSA-REI.B.4.b: 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.

Use Khan Academy

Students will analyze the graphs of quadratic functions by identifying the maximum or minimum value of the functions. This will allow for deeper understanding when analyzing polynomial functions of higher degree and real life applications such as the position of a free falling object.

Quadratic functions can be used to model the design of a room. For instance, exercise 59 on page 97 shows how the size of an indoor fitness room with a running track can be modeled.

When completing the square, some students forget to multiply the subtracted square by the value factored out of the x terms. Remind students to be sure that they are adding and subtracting the same value to maintain equality.

To help visual learners, display several graphs of various vertical and horizontal translations of a parabola. Have students practice identifying the vertex and x-intercepts of each parabola. Then have students use the vertex and x-intercepts to write the equation of each parabola.

Use common assessments

PreCalc with Limits