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Chapter 2: Problem 59

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 \(f(x)=0\). $$f(x)=x^{2}-4 x$$

Short Answer

Expert verified
The x-intercepts of the function \(f(x)=x^{2}-4x\) are x = 0 and x = 4 as shown both by the graph and by setting \(f(x)\) equal to 0 and solving for x.

Step by step solution

01

Graph the Quadratic Function

To start, you need to graph the quadratic function \(f(x)=x^{2}-4x\). This will give you a picture of what you are looking for.
02

Find the x-intercepts by Setting \(f(x)\) to 0

Once you have graphed the function, you will need to find the x-intercepts. These are the points where the graph crosses the x-axis. You do this by setting \(f(x)\) to 0 and then solving the equation for x. So, set \(x^2 - 4x = 0\).
03

Solve for x

To solve \(x^{2}-4x=0\) for x, you can factor it to \(x(x - 4) = 0\). Using the zero product property, you set each factor equal to zero and solve for x. This gives you that x = 0 and x = 4.
04

Compare with Graph

Pick those values of x (x = 0 and x = 4) and plug it back into the function \(f(x)=x^{2}-4x\). Both will yield 0, validating that the x-intercepts of the graph are x = 0 and x = 4. The solutions of the corresponding equations when \(f(x)=0\) are confirmed by the graph.

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