Working with polynomial functions and their graphs complete solutions correct answers key

Working with polynomial functions and their graphs complete solutions correct answers key

(Note comments in brackets [?] should be pondered; you need not submit a response.)

Introduction, working with a quadratic function:

Consider the function

1. By inspection, we see this is a quadratic function (or 2nd degree polynomial function) [why?] and its graph is a parabola

that opens upwards.

We also know the intercept

is . [why?]

2. This particular function may be factored relatively nicely and we see that .

Thus, the zeros of the function are x = 1 and x = 5 [why?]

If you were to graph this function, the xintercepts

are located at (1, 0) and 5, 0).

Furthermore, the axis of symmetry is or

3. By completing the square, we can write the function as . [Can you do this?]

Thus the vertex of the parabola is located at the point .

4. Using the work above, a short analysis (quick sketch of the function) will help answer many questions:

Quick sketch based upon the prior information:

We can answer such questions as:

a) Where is decreasing? b) Where is ?

4 problems