Question

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{9.2-x}=1.8$$

Short answer

The solution is the \(x\) value at the intersection point of the functions. After checking algebraically by squaring both sides of the equation and solving for \(x\), the answer obtained should match the \(x\) value at which the functions intersect graphically. The graphing calculator makes the process of finding the intersection point much easier.

Step-by-step solution

Graphing the function

Enter \(y=\sqrt{9.2-x}\) and \(y=1.8\) into the graphing calculator to graph the functions. Two lines will be generated, one representing the square root function and the other representing the constant function \(y=1.8\). The solution to the problem is the \(x\) value at which these two lines intersect.

Finding the intersection point

Using the intersection function on the graphing calculator, determine the \(x\) value at the intersection point to find the solution. This should be the point where the two functions cross each other.

Checking the solution algebraically

Square both sides of the equation \(y=\sqrt{9.2-x}=1.8\) to get \(9.2-x = 1.8^2\). Solve this equation to get the value of \(x\), which should match the intersection point found in step 2. Squaring both sides removes the square root, making it easier to solve the equation algebraically.