Chapter 3

Question 1

Polynomial Function

Answer 1

A polynomial function f of degree n, where n is a nonnegative integer, is given by f (x) = an(subscript)x^n + an-1(subscript)x^n-1 + L + a1(subscript)x + a0(subscript)
when an(subscript), an-1(subscript),..., a1(subscript), and a0(subscript) are real numbers, with an(subscript) ≠ 0

Question 2

Quadratic Function

Answer 2

A function f is a quadratic function if f(x) = ax^2 + bx + c
where a, b, and c are real numbers, with a ≠ 0.

Question 3

Applying Graphing Techniques to a Quadratic Function

Answer 3

Compared to the basic graph of f(x) = x^2, the graph of F(x) a (x-h)^2 + k has the following characteristics.
Vertex Form: a(x-h)^2 + k

a:

• Opens up if a > 0
• Opens down if a 0
• Vertically shrunk (wider) if 0 0
• |h| units left if h 0
• |k| units down if k

Question 4

Graph of a Quadratic Function

Answer 4

The quadratic function defined by f(x) = ax^2 + bx + c can be written as y = f (x) = a (x-h)^2 +k , a ≠ 0
where h = (-b/2a) and k = f (h)

The graph of f has the following characteristics

1. It is a parabola with vertex (h, k) and the vertical line x = h as axis
2. It opens up if a > 0 and down is a 1
3. The y-intercept is f(0) = c
4. The x-intercepts are found by solving the equation ax^2 + bx + c = 0

If b^2 -4ac > 0, the x-intercepts are (-b +- b^2 -4ac (sqrt)) / 2a

If b^2 -4ac = 0, the x-intercept is -(b/2a)

If b^2 -4ac