Solving Equations Graphically

Solving equations graphically involves selecting x-values, calculating corresponding y-values from the equation, and plotting these points on a coordinate plane to draw the graph.

The solutions to the equation are the x-values where the graph intersects the x-axis, as these points show where the equation equals zero.

This method is also useful for solving quadratic equations. The number of times the graph of a quadratic equation touches or crosses the x-axis shows the number of real solutions the equation has.

If it doesn’t touch at all, there are no real solutions.

To solve an equation within a specific interval of x-values, the graph is restricted to x-values within that interval.

Only the x-intercepts inside this interval are considered valid solutions.

To solve a system of two equations graphically, both equations are plotted. The point where the two graphs intersect gives the solution that satisfies both equations.

In business, total cost and total revenue are plotted against units sold. Their graphs intersect at the break-even point—where revenue equals cost for a specific number of units.