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h(x)=-5(x-1)^(2)+7 A fountain sprays a constant stream of water from a nozzle. The function shows h, the height of the stream of water in feet above the water surface, in relation to x, the horizontal distance in feet from the nozzle. What is the best interpretation of the number 7 in the function? Choose 1 answer: (A) The stream of water begins at an initial height of 7 feet above the surface. (B) The stream of water will reach a maximum height of 7 feet above the surface. (C) The stream of water will touch the surface at a distance of 7 feet horizontally from the nozzle. (D) The stream of water will reach a maximum height at a distance of 7 feet horizontally from the nozzle.

h(x)=−5(x−1)2+7 h(x)=-5(x-1)^{2}+7 \newlineA fountain sprays a constant stream of water from a nozzle. The function shows h h , the height of the stream of water in feet above the water surface, in relation to x x , the horizontal distance in feet from the nozzle. What is the best interpretation of the number 77 in the function?\newlineChoose 11 answer:\newline(A) The stream of water begins at an initial height of 77 feet above the surface.\newline(B) The stream of water will reach a maximum height of 77 feet above the surface.\newline(C) The stream of water will touch the surface at a distance of 77 feet horizontally from the nozzle.\newline(D) The stream of water will reach a maximum height at a distance of 77 feet horizontally from the nozzle.

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Q. h(x)=−5(x−1)2+7 h(x)=-5(x-1)^{2}+7 \newlineA fountain sprays a constant stream of water from a nozzle. The function shows h h , the height of the stream of water in feet above the water surface, in relation to x x , the horizontal distance in feet from the nozzle. What is the best interpretation of the number 77 in the function?\newlineChoose 11 answer:\newline(A) The stream of water begins at an initial height of 77 feet above the surface.\newline(B) The stream of water will reach a maximum height of 77 feet above the surface.\newline(C) The stream of water will touch the surface at a distance of 77 feet horizontally from the nozzle.\newline(D) The stream of water will reach a maximum height at a distance of 77 feet horizontally from the nozzle.
  1. Understand Function Components: Analyze the function h(x)=−5(x−1)2+7h(x) = -5(x-1)^2 + 7 to understand its components.\newlineThe function is in the vertex form of a parabola, a(x−h)2+ka(x-h)^2 + k, where:\newline- aa is the coefficient that determines the direction and width of the parabola,\newline- (h,k)(h, k) is the vertex of the parabola.\newlineIn this case, a=−5a = -5, h=1h = 1, and k=7k = 7.\newlineSince aa is negative, the parabola opens downwards.
  2. Significance of Number 77: Determine the significance of the number 77 in the context of the function.\newlineThe number 77 is the value of kk in the vertex form of the parabola, which represents the yy-coordinate of the vertex. Since the parabola opens downwards, the vertex is the maximum point of the parabola.
  3. Interpret Vertex: Interpret the vertex in the context of the water stream from the fountain. The vertex (1,7)(1, 7) indicates that the maximum height of the water stream is 77 feet above the water surface, and this maximum height is reached at a horizontal distance of 11 foot from the nozzle.
  4. Match Interpretation: Match the interpretation of the number 77 with the given answer choices.\newlineThe correct interpretation of the number 77 is that it represents the maximum height of the water stream above the surface. This matches with answer choice (B).

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