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.
Accepted Solution
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Answer:The maximum height of the puck is 4 feet. −(x − 4)^2 + 6Step-by-step explanation:we have[tex]f(x)=-x^{2}+8x-10[/tex]This is the equation of a vertical parabola open downwardthe vertex is a maximumConvert to vertex form[tex]f(x)+10=-x^{2}+8x[/tex]Factor -1 the leading coefficient[tex]f(x)+10=-(x^{2}-8x)[/tex]Complete the square[tex]f(x)+10-16=-(x^{2}-8x+16)\\ f(x)-6=-(x^{2}-8x+16)[/tex]Rewrite as perfect square[tex]f(x)-6=-(x-4)^{2}\\ f(x)=-(x-4)^{2}+6[/tex]The vertex is the point (4,6)thereforeThe maximum height of the puck is 4 feet.