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Chapter 2: Problem 88

Find the vertex for each parabola. Then determine a reasonable viewing rectangle on your graphing utility and use it to graph the quadratic function. $$y=0.01 x^{2}+0.6 x+100$$

Short Answer

Expert verified
The vertex of the parabola is (-30, 100). A reasonable viewing rectangle on a graphing utility would be [-40, -20] for x range and [90, 110] for y range. You can then graph the parabola using these parameters.

Step by step solution

01

Finding the Vertex

The quadratic equation provided is in the standard form \( y = ax^2+bx+c \), where a = 0.01, b = 0.6 and c = 100. The formula for finding the vertex is \( h = -\frac{b}{2a} \), \( k = f(h) \). So, let's find h first: \( h = -\frac{b}{2a} = -\frac{0.6}{2(0.01)} = -30 \). Now, substitute h into the equation to find k: \( k = f(-30) = 0.01(-30)^2 + 0.6(-30) + 100 = 100 \). Therefore, the vertex of the parabola is (-30, 100)
02

Determining a Viewing Rectangle

After finding the vertex, the next step is to find a viewing rectangle for graphing the quadratic function. A recommended viewing rectangle would be one that allows for observation of the vertex and the behavior of the parabola at least a little on both sides of the vertex. Given the vertex coordinate (-30,100), [-40, -20] for x range and [90, 110] for y range would be a reasonable viewing rectangle.
03

Graphing the Quadratic Function

Graph the function \(y=0.01 x^{2}+0.6 x+100\) within the viewing rectangle. Plot the vertex (-30, 100), and then plot points on either side of the vertex using the quadratic equation to find y values. This will help construct the curve of the parabola.

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