Suppose that a quadratic equation had two x-intercepts. How could you use the intercepts to find the vertex?
take the midpoint of the x-intercepts to get the x value of the vertex,
sub in that x value to get the y.
To find the vertex of a quadratic equation using the x-intercepts, you can follow these steps:
1. Determine the x-values of the intercepts. Let's say the two x-intercepts are denoted as x1 and x2.
2. Calculate the x-coordinate of the vertex. The x-coordinate, denoted as "h," can be found by taking the average of the two intercepts using the formula: h = (x1 + x2) / 2.
3. Evaluate the y-coordinate of the vertex. To find the y-coordinate, substitute the value of h into the quadratic equation to find the corresponding y-value. This can be calculated as y = f(h), where f(x) represents the quadratic equation.
By following these steps, you can determine the vertex of the quadratic equation using the given x-intercepts.