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Chapter 1: Problem 17

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$g(x)=-2 x^{2}$$

Short Answer

Expert verified
The graph of the function \(g(x) = -2x^{2}\) is a downward-opening parabola with its vertex at the origin. An appropriate viewing window might be -10 to 10 on both the x and y axes.

Step by step solution

01

Identify the vertex

A vertex for a quadratic function in standard form \(y = ax^{2} + bx + c\) is given by the point \((h, k)\), where \(h = -b/2a\) and \(k = f(h)\). Since this is a basic quadratic function without constant and linear terms, the vertex is at the origin, (0, 0).
02

Identify the direction of the parabola

The coefficient of \(x^{2}\) is -2. Since this is negative, the parabola will open downwards.
03

Choose an appropriate viewing window

For this function, an appropriate viewing window might be -10 to 10 on both the x and y axes. This allows us to see the complete graph of the function.
04

Graph the function

Using a graphing utility, input the function \(g(x) = -2x^{2}\) with the viewing window described in the previous step. The result should be a downward-opening parabola with its vertex at the origin.

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