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Chapter 3: Problem 85

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 quadratic function is \((-30, 90)\). A suitable viewing rectangle on a graphing utility for this function would be the range [=[-40, -20] for the x-axis and the range={[80, 100] for the y-axis.

Step by step solution

01

Calculate the vertex

The vertex of the quadratic function \( y = ax^{2} + bx + c \) is given by the point (h, k), where h is given by the formula \( -b/(2a) \), and k is \( y(h) \). Given that \( a = 0.01 \), \( b = 0.6 \) and \( c = 100 \), we can calculate the x-coordinate of the vertex h as \( h = -b/(2a) = -0.6/(2 * 0.01) = -30 \). Substitute \( h = -30 \) into the equation to calculate k. Therefore, \( y(-30) = 0.01(-30)^{2} + 0.6(-30) + 100 = 90 \). Hence, the vertex of the quadratic function is \((-30, 90)\).
02

Identify a suitable viewing rectangle

Knowing the vertex \((-30, 90)\), and considering patterns of quadratics, a suitable viewing rectangle would be one that includes the vertex with an appropriate range on both sides of the x coordinate (-30) and y coordinate (90). Considering the range [=[-40, -20] for x-axis and [=[80, 100] for y-axis should sufficiently capture the curve of the parabola.

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Most popular questions from this chapter

The rational function $$f(x)-\frac{27,725(x-14)}{x^{2}+9}-5 x$$ models the number of arrests, \(f(x)\), per \(100,000\) drivers, for driving under the influence of alcohol, as a function of a driver's age, \(x\). a. Graph the function in a \([0,70,5]\) by \([0,400,20]\) viewing rectangle. b. Describe the trend shown by the graph. c. Use the ZOOM and TRACE features or the the maximum function feature of your graphing utility to find the age that corresponds to the greatest number of arrests. How many arrests, per \(100,000\) drivers, are there for this age group?

If you are given the equation of a rational function, explain how to find the vertical asymptotes, if there is one, of the function's graph.

Describe how to graph a rational function.

Solve each inequality in Exercises \(65-70\) and graph the solution set on a real number line. $$ \frac{3}{x+3}>\frac{3}{x-2} $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I like to think of a parabola's vertex as the point where it intersects its axis of symmetry.
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