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Chapter 1: Problem 59

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y=x^{2}-4 x+3$$

Short Answer

Expert verified
The graph of \(y=x^{2}-4x+3\) is a parabola. The x-intercepts can be found by setting \(y=0\) and solving for \(x\), and the y-intercept can be found by setting \(x=0\) and solving for \(y\). Based on shape of the graph, the x-intercepts are approximate values at \(x = 1\) and \(x = 3\), and y-intercept is at \(y = 3\).

Step by step solution

01

Identify the equation:

The quadratic equation given here is \(y = x^{2} - 4x + 3\).
02

Enter the equation into a graphing utility

Use a graphing calculator or an online graphing utility and input the equation \(y=x^{2}-4 x+3\). Then press the graph button (or the equivalent) to generate a graph of the function.
03

Finding the x-intercepts

The x-intercepts are the points where our graph crosses the x-axis, i.e., when \(y=0\). If the graph doesn't directly show these points, we need to use the fact that x-intercepts are the solutions of the equation \(0=x^{2}-4 x+3\). Solving this quadratic equation will give us the x-intercepts.
04

Finding the y-intercepts

The y-intercepts are the points where our graph crosses the y-axis, i.e., when \(x=0\). By substituting \(x=0\) into our equation, we get \(y=0^{2}-4*0+3\), which equals 3. Hence, the y-intercept is (0,3).
05

Reading the graph

Having plotted the graph with a graphing utility and found the x and y-intercepts, we should now be able to approximate the points where the graph intersects the x and y axes.

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