Solve the equation and graphing utility to verify your solution
To solve an equation and verify the solution using a graphing utility, you can follow these steps:
1. Write down the equation you want to solve.
2. Use algebraic methods to isolate the variable on one side of the equation.
3. Simplify the equation as much as possible.
4. Determine the value(s) of the variable that make the equation true.
5. Plot the graph of the equation using a graphing utility.
6. Verify that the solution you found in step 4 is consistent with the graph.
Let's demonstrate this process with an example equation: x^2 - 4 = 0.
1. The equation we want to solve is x^2 - 4 = 0.
2. To isolate the variable, we can add 4 to both sides of the equation: x^2 = 4.
3. The equation is now simplified.
4. To determine the values of x that make the equation true, we can take the square root of both sides: x = ±2.
Therefore, x = 2 or x = -2 are the solutions to the equation.
5. We can now plot the graph of the equation y = x^2 - 4 using a graphing utility.
6. The graph will show that the equation intersects the x-axis at x = 2 and x = -2, confirming our solutions.
By following these steps, you can solve an equation and use a graphing utility to verify your solution.