Suzanne W.

Fill in the blanks.

The graph of a quadratic function is symmetric about its ________.

In Exercises 13-16, graph each function. Compare the graph of each function with the graph of $ y = x^2 $.

(a) $ f(x) = -\frac{1}{2} (x - 2)^2 + 1 $
(b) $ g(x) = \left[\frac{1}{2} (x -1) \right]^2 - 3 $
(c) $ h(x) = -\frac{1}{2} (x +1)^2 - 1 $
(d) $ k(x) = [2(x + 1)]^2 +4 $

In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s).

$ f(x) = -\frac{1}{3} x^2 + 3x - 6 $

In Exercises 47-56, write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point.

Vertex: $ ( 4, -1 ) $; point: $ ( 2, 3 ) $

A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals (see figure).

(a) Write the area $ A $ of the corrals as a function of $ x $.
(b) Create a table showing possible values of $ x $ and the corresponding areas of the corral. Use the table to estimate the dimensions that will produce the maximum enclosed area
(c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions that will produce the maximum enclosed area.
(d) Write the area function in standard form to find analytically the dimensions that will produce the maximum area.
(e) Compare your results from parts (b), (c), and (d).

In Exercises 55 - 58, use a graphing utility to graph the equation. Use the graph to approximate the values of $ x $ that satisfy each inequality.

Equation
$ y = \dfrac{2x^2}{x^2 + 4} $

Inequalities
$ (a) $ y \ge 1 $ (b) $ y \le 2 $