The height of a hockey puck that is hit toward a goal is modeled by the function f(x) = −x^2 + 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.

-(x - 4)² + 6

Max height: 6

Step-by-step explanation:

Step 1: Factor out negative

0 = -(x² - 8x + 10)

Step 2: Divide by -1

0 = x² - 8x + 10

Step 3: Move 10 over

-10 = x² - 8x

Step 4: Complete the Square

-10 + 16 = x² - 8x + 16

6 = (x - 4)²

Step 5: Move 6 over

(x - 4)² - 6

Step 6: Multiply by -1

-(x - 4)² + 6

The maximum height of the puck is 6 feet. We look at k in f(x) = a(bx - h)² + k.

-(x-4)^2+6=0

maximum point (4,6)

max=6

Step-by-step explanation:

−x^2 + 8x − 10 use the formula (b/2)^2 to create a new term to complete the square: b=8 so the new term is (8/2)^2 = 16

−x^2 + 8x − 10+16=0

factorize : -x^2+8x+16-10

-(x-4)^2+6=0

to find the maximum value : x= -b/2a b=8 and a=-1

x=-8/-2

x=4 substitute the value of x in the equation:

-4^2+8(4)-10=-16+32-10=6

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)