To find the maximum height of the puck, we first need to complete the square for the function f(x) = -x^2 + 8x - 10.
Starting with -x^2 + 8x - 10, we want to rewrite this in the form -(x - h)^2 + k, where (h, k) is the vertex of the parabola.
To complete the square, we need to factor out the coefficient of x^2 from the x terms:
-x^2 + 8x - 10 = -(x^2 - 8x) - 10
Next, we want to add and subtract (8/2)^2 = 16 to complete the square:
= -(x^2 - 8x + 16 - 16) - 10
= -(x - 4)^2 + 16 - 10
= -(x - 4)^2 + 6
Therefore, the function can be rewritten as f(x) = -(x - 4)^2 + 6. The maximum height of the puck is located at the vertex of the parabola, which is located at (4, 6).
So, the correct answer is: -(x − 4)^2 + 6; The maximum height of the puck is 6 feet.
The height of a hockey puck that is hit toward a goal is modeled by the function f(x) = −x2 + 8x − 10, where x is the distance from the point of impact. Complete the square to determine the maximum height of the path of the puck.
−(x − 4)2 + 26; The maximum height of the puck is 26 feet.
−(x − 4)2 + 26; The maximum height of the puck is 4 feet.
−(x − 4)2 + 6; The maximum height of the puck is 4 feet.
−(x − 4)2 + 6; The maximum height of the puck is 6 feet.
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