Question

What is the process of finding the vertex when given the x-intercepts (3,0) and (9,0)?

a) Calculate the average of the x-intercepts.
b) Use the midpoint formula for the x-values.
c) The vertex is the point at the midpoint of the x-intercepts.
d) Find the slope between the x-intercepts and use it to determine the vertex.

Answer 1

The vertex can be found by calculating the midpoint of the x-intercepts. Take the average of the x-values from the intercepts; in this case, the vertex's x-coordinate is 6. The y-coordinate requires further information from the parabola's equation.

Step-by-step explanation:

The process of finding the vertex when given the x-intercepts is to calculate the midpoint of the x-intercepts. For x-intercepts at (3,0) and (9,0), the process involves finding the average of the x-values.

Here is a step-by-step explanation:

1. Calculate the average of the x-coordinates of the given x-intercepts: (3 + 9) / 2 = 12 / 2 = 6.
2. The midpoint of (3,0) and (9,0) on the x-axis is 6, so this is the x-coordinate of our vertex.
3. Since the given x-intercepts are for a parabola, and the vertex is equidistant from both, we then find the parabola's equation to determine the y-coordinate of the vertex, which is not provided in the question. However, if you have the equation of the parabola, you can substitute x = 6 into the equation and solve for the y-coordinate.

The resulting vertex of the parabola will have an x-coordinate of 6 and some y-coordinate that depends on the specific parabola's equation.