If you are looking at a graph of a quadrtic equation, how do you determine where the solutions are?
The solutions are the x values where y = 0. (Where the curve crosses the x axis). y is the quadratic function.
The solutions are found at the location
(x ,0), where x represents any value and 0 represents the y coordinate.
Three samples:
(4, 0), (-6, 0) and (-1/2, 0)
To determine the solutions of a quadratic equation by looking at its graph, you need to identify the x-coordinates of the points where the graph intersects the x-axis. These points are also known as the x-intercepts or roots of the equation.
Here are the steps to determine the solutions from the graph:
1. Locate the x-intercepts: Examine the portion of the graph that intersects or touches the x-axis. These points will have a y-coordinate of 0. Identify the x-values (or the values on the x-axis) at these points.
2. Note the number of intercepts: Count the number of x-intercepts on the graph. There can be three possibilities:
- Two intercepts: If the graph intersects the x-axis at two distinct points, the quadratic equation has two real solutions.
- One intercept: If the graph only touches the x-axis at a single point, the quadratic equation has one real solution (known as a double root).
- No intercepts: If the graph does not intersect or touch the x-axis, the quadratic equation has no real solutions.
3. Determine the x-coordinate values: Once you have identified the x-coordinates of the intercepts, these values represent the solutions to the quadratic equation.
It's important to note that sometimes the graph is not easily readable, or it may intersect the x-axis outside the visible portion of the graph. In such cases, you might need to use other methods like factoring, completing the square, or using the quadratic formula to find the equation's solutions.