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A football is kicked in the air, and it’s path can be modeled by the equation f(x) = -2(x-3)2 + 56 where x is the horizontal distance, in feet, and f(x) is the height, in feet. What is the maximum height reached by the football?

User Fishbacp
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2 Answers

4 votes

Answer:

Maximum height = 56 feet

Explanation:

The equation is in the vertex form of the quadratic equation, whose general form is:

y = a(x - h)^2 + k, where

  • a determines whether the parabola opens upward or downward (positive a signifies minimum and negative a signifies minimum),
  • and (h, k) is the vertex (either a minimum or maximum).

Thus, in the equation f(x) = -2(x -3)^2 + 56, (3, 56) is the equation of the vertex (in this case the maximum) and since f(x) represents the height in feet, the max height reached by the football is 56 feet.

User Tiff
by
7.5k points
1 vote

Answer:

The given equation for the path of the football is f(x) = -2(x-3)^2 + 56.

This is a quadratic function in the form f(x) = a(x-h)^2 + k, where a, h, and k are constants.

Comparing this equation to the standard form, we can see that a = -2, h = 3, and k = 56.

Since the coefficient of the squared term is negative, the graph of this quadratic function is a downward-facing parabola.

The maximum height reached by the football occurs at the vertex of the parabola.

The x-coordinate of the vertex is given by x = h = 3.

The y-coordinate of the vertex is given by f(h) = k = 56.

Therefore, the maximum height reached by the football is 56 feet.

Explanation:

User Ernani
by
8.2k points

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