Question

Use a graphing calculator to approximate the solution of the equation. $$ x^{2}+6 x-7=0 $$

Short answer

Using a graphing calculator to solve the quadratic equation \(x^{2} + 6x - 7 = 0\), the solutions (to an approximation) are the x-coordinates where the function graph crosses the x-axis.

Step-by-step solution

Input the Equation into the Graphing Calculator

Input the equation \(x^{2} + 6x - 7 = 0\) into the graphing calculator.

Graph the Equation

Use the calculator's graphing function to display the graph. The graph is a parabola that opens upwards due to the positive coefficient of the leading term \(x^{2}\). The solutions to the equation are the x-coordinates where the graph crosses the x-axis.

Find the Solutions

Use the calculator's root finding or zero crossing points function to find the solutions. The root function on a graphing calculator finds the x-values where the function has a value of zero. This is done by identifying one point to the left and one point to the right of the point where the graph is crossing the x-axis, and instruct the calculator to find the root in that interval.