What does it mean to give the solutions to the following quadratic equation by examining the graph of the related quadratic function:
Graph: y = x^2 + 2x - 15
Equation: x^2 + 2x - 15 = 0
To give the solutions to the quadratic equation x^2 + 2x - 15 = 0 by examining the graph of the related quadratic function y = x^2 + 2x - 15, you can look for the x-coordinates where the graph intersects the x-axis. These intersection points represent the solutions to the equation.
Here's how you can find the solutions using the given graph:
1. Plot the graph: Start by plotting the quadratic function y = x^2 + 2x - 15 on a coordinate plane. To do this, mark some points on the graph by substituting different x-values into the equation and finding the corresponding y-values. Connect the plotted points to get a smooth curve.
2. Locate the x-intercepts: The x-intercepts are the points where the graph intersects the x-axis. In other words, these are the values of x for which the corresponding y-values are equal to zero (y = 0).
3. Analyze the x-intercepts: Determine the x-values of the points where the graph crosses the x-axis. These x-values are the solutions to the quadratic equation.
In the given equation x^2 + 2x - 15 = 0, the solutions are the values of x that satisfy the equation.
By examining the graph, you can see that the graph intersects the x-axis at two points. These points are (-5, 0) and (3, 0). Therefore, the solutions to the quadratic equation x^2 + 2x - 15 = 0 are x = -5 and x = 3.