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Chapter 9: Problem 94

Use a graphing utility to solve \(4-(x+1)^{2}=0 .\) Graph \(y=4-(x+1)^{2}\) in a \([-5,5,1]\) by \([-5,5,1]\) viewing rectangle. The equation's solutions are the graph's \(x\) -intercepts. Check by substitution in the given equation.

Short Answer

Expert verified
The solutions to the equation are the x-values where the graph intersects the x-axis. They can be verified by substituting back into the original equation.

Step by step solution

01

Identify the equation

The given equation is \(4-(x+1)^{2}=0.\) This is a quadratic equation with solutions found where it intersects the x-axis on a graph.
02

Plot the equation

Use a graphing utility to graph the equation \(y=4-(x+1)^{2}\) within the viewing rectangle defined by \([-5,5,1]\) by \([-5,5,1]\). Look for the points where the graph intersects the x-axis, as these points represent the solutions to the equation.
03

Find the x-intercepts

Identify the x-intercepts of the graph. The x-intercepts are the values of x for which y is 0. These are the solutions to the original equation.
04

Check the solution

Substitute the found x-values back into the original equation \(4-(x+1)^{2}=0.\) If both sides of the equation are equal, then the found solutions are correct.

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