Question

The path of a water sprinkler is designed to reach a maximum height of 7 feet after 1 second. The sprinkler is 0.5 feet off the ground. If the water pressure increases, the water exceeds the intended height. Complete the values for the inequality in vertex form to describe the points that are greater than the original projected path. y a(x – h)2 + k a = h = k =

Answer 1

The path of the water sprinkler can be described by the equation y = a(x - h)^2 + k. To find the inequality for points above the original projected path, we need to consider a new vertex with a greater y-coordinate. The inequality is y > a(x - 1)^2 + 7.

Step-by-step explanation:

The path of the water sprinkler can be described by the equation y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the maximum height of the water is 7 feet after 1 second, which means (h, k) = (1, 7).

The sprinkler is initially 0.5 feet off the ground, so the equation becomes y = a(x - 1)^2 + 7, and we need to find the value of a.

To determine the inequality, we need to consider values of y that are greater than the original projected path. This means the vertex of the new parabola will have a greater y-coordinate than the original vertex, which is (1, 7).

Since the new parabola is shifted upwards, the new vertex will be (1, k), where k > 7.

The value of k is determined by the water pressure increase. Therefore, we can write the inequality as y > a(x - 1)^2 + 7, where a is the coefficient of the quadratic term.