jpmoney306
contestada

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.

Respuesta :

calculista

Answer:

The maximum height of the puck is 4 feet. −(x − 4)^2 + 6

Step-by-step explanation:

we have

[tex]f(x)=-x^{2}+8x-10[/tex]

This is the equation of a vertical parabola open downward

the vertex is a maximum

Convert 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)

therefore

The maximum height of the puck is 4 feet.

WonderBat

Answer:

−(x − 4)2 + 6; The maximum height of the puck is 6 feet.

Step-by-step explanation:

Use the formula  ( b /2 ) ^2  in order to create a new term to complete the square.

Hope this helped!

Otras preguntas