Course 1, Unit 7 - Quadratic Functions
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.)