Sure! The error message "ERR: NO SIGN CHNG" indicates that the graphing calculator cannot determine the solutions to the equation because there is no change in sign on the graph. This means that the quadratic equation you entered does not intersect the x-axis, meaning it has no real solutions.
Let's go through the steps to find the correct solutions to the quadratic equation (5x^2 - 80 = 0) using the TI-83 calculator:
1. Turn on your calculator and press the "MODE" button. Make sure you are in "Function" mode (Func), which is usually the first option.
2. Press the "Y=" button to enter the equation editor. Clear any existing equations by pressing the "Clear" button if necessary.
3. Enter the quadratic equation: 5x^2 - 80. You do not need to include "=0" because the calculator assumes the equation equals zero.
4. Press the "GRAPH" button to plot the graph of the equation.
5. Inspect the graph to see if it intersects or touches the x-axis. If you see that the graph does not cross or touch the x-axis, it means that the equation has no real solutions, which is consistent with the "ERR: NO SIGN CHNG" error message you received.
In this case, your quadratic equation (5x^2 - 80) does not have any real solutions. It represents a parabola that opens upward and does not intersect the x-axis.
Therefore, the correct answer is that the equation has no solutions, rather than (-4 and 4) as you mentioned.