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Chapter 2: Problem 60

Use a graphing utility to graph the quadratic function. Find the \(x\) -intercept(s) of the graph and compare them with the solutions of the corresponding quadratic equation when \(f(x)=0\). $$f(x)=-2 x^{2}+10 x$$

Short Answer

Expert verified
The x-intercepts of the function \(f(x)=-2 x^{2}+10 x\) are \(x=0\) and \(x=5/2\). These are also the solutions to the equation when \(f(x)=0\). Upon plotting the graph, the same x-intercepts are observed.

Step by step solution

01

Graph the Function

Based on the function \(f(x)=-2 x^{2}+10 x\), use a graphing utility to plot the function. From the graph, determine the x-intercepts, which are the points where the curve intersects or crosses the x-axis.
02

Calculate x-intercepts Algebraically

To determine the x-intercepts algebraically, set \(f(x) = 0\) and solve for \(x\). So, the equation becomes: \[0 = -2 x^{2}+10 x\]. Factorize the equation to get \(x(5 - 2x) = 0\). This gives us two possible solutions for x, x=0 and x=5/2.
03

Compare the Solutions

Compare the x-intercepts from the graph with the solutions calculated algebraically. Both the methods should yield the same x-intercepts.

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Most popular questions from this chapter

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