Problem 94 - Introductory Algebra for College Students

Question

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.

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.

Step 4: 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.