Course 1, Unit 7 - Quadratic Functions

Overview
In conventional high school algebra curricula, the most prominent nonlinear expressions and functions are quadratic polynomials. In Core-Plus Mathematics Course 1, earlier and greater attention is given to Exponential Functions due to their relevance and to capitalize on the connections with linear functions. This unit begins the study of Quadratic Functions that will be continued in Core-Plus Mathematics Courses 2-4. Thus, this unit should be treated as an introduction to Quadratic Functions.

To be proficient in the use of quadratic functions for problem solving, students must have a clear and connected understanding of the numeric, graphic, verbal, and symbolic representations of quadratic functions and the ways that those representations can be applied to patterns in real data. The lessons of this unit are planned to develop each student’s intuitive understanding of quadratic patterns of change and technical skills for reasoning with the various representations of those patterns. Understanding and skill in working with quadratic functions is developed in three lessons.

Key Ideas from Course 1, Unit 7

• Quadratic function rule: a function with equation in the form y = ax² + bx + c. The relationship between height (in feet) of a kicked ball and its time in flight (in seconds) is modeled reasonably well by a quadratic function. For example, if h = -16t² + 50t + 3, the ball's height in feet after t seconds depends on the initial height (3 feet in this example), the initial velocity of the ball (50 ft/sec in this example), and the effect of gravity (indicated by the -16 ft/sec in this example).

• Quadratic function graph:

  

• Quadratic function table:

  

• Expanding and factoring quadratic expressions: Applications of the distributive property are used to multiply two binomial expressions and to factor binomials and trinomials. (See pp. 491-498. See Strategies I and II on p. 497.)

• Identify the maximum or minimum points and x-intercepts: Students use factoring techniques, symmetry, and/or the quadratic formula to find key points on a quadratic graph. (See pp. 492-498.)

• Solve quadratic equations: Quadratic equations of the form ax² + c = d, ax² + bx = 0, and ax² + bx + c = d are solved symbolically and by using the quadratic formula. This topic is practiced in various Review tasks and further developed in subsequent units. (See pp. 510-517.)