Introduction to Quadratics Exploration
- David Hornbeck
MAJOR NOTE FOR THIS ASSIGNMENT: All of the CAPITALIZED WORDS are vocabulary words. On a scratch sheet of paper, write these words down as well as their corresponding definition. THEN move forward and answer the questions at the below the graphic. You must have both the definitions and the questions answered to get full credit for the homework. Any function that has a DEGREE (the highest exponent of a polynomial) of 2 is called a QUADRATIC FUNCTION. Functions are written as f(x) = OR y = . In this sketch, it is written as f(x). The shape of the graph of a quadratic (the curve you see) is called a PARABOLA. In this sketch, I want you to investigate what the COEFFICIENTS of the terms (variables) in the quadratics do to the parabola.
The very first quadratic shown - when a = 1, b = 0, and c = 0 - is the PARENT of all quadratic functions. It is the basic function, y = (x squared). All other quadratics can be formed by transforming this parent function (that's why it's called the parent!). Answer the following questions. Try to use words like "stretch," "shrink," "translate," "x-intercept," and "y-intercept." 1. Adjust the a slider. This is the coefficient of the (x-squared) term. What happens to the parabola as you change a? Be specific. 2. Adjust the b slider. This is the coefficient of the x term. What happens to the parabola as you change b? Be specific. 3. Adjust the c slider. This is called the CONSTANT term (because it is just a number; it is constant because it is not a variable and thus cannot vary). What happens to the parabola as you change c? Be specific.