6)
A teenager who is 5 feet tall throws an object into the air. The quadratic function f(x)=−16x2+64x+5
is where f(x)
is the height of the object in feet and x
is the time in seconds.
The function in vertex form is
(1 point)
Responses
f(x)=−16(x−2)2+5
f of x is equal to negative 16 times open paren x minus 2 close paren squared plus 5
f(x)=−16(x−2)2 −11
f(x)=−16(x−2)2 −11
f(x)=−16(x−2)2+69
f of x is equal to negative 16 times open paren x minus 2 close paren squared plus 69
f(x)=−16(x−2)2−59
f of x is equal to negative 16 times open paren x minus 2 close paren squared minus 59
Question 2
(1 point)
The object hits the ground after about
seconds.
The object hits the ground after about 3 seconds.
This can be calculated by setting the function equal to 0 and solving for x:
-16x^2 + 64x + 5 = 0
Using the quadratic formula, we get:
x = (-64 ± √(64^2 - 4(-16)(5))) / 2(-16)
x = (-64 ± √(4096 + 320)) / -32
x = (-64 ± √4416) / -32
x = (-64 ± 66.54) / -32
x = (-64 + 66.54) / -32 or x = (-64 - 66.54) / -32
x = 2.54 / -32 or x = -130.54 / -32
x = -0.079375 or x = 4.079375
Since time cannot be negative, the object hits the ground after about 4 seconds.
6)
A teenager who is 5 feet tall throws an object into the air. The quadratic function f(x)=−16x2+64x+5
is where f(x)
is the height of the object in feet and x
is the time in seconds.
The function in vertex form is
(1 point)
Responses
f(x)=−16(x−2)2+5
f of x is equal to negative 16 times open paren x minus 2 close paren squared plus 5
f(x)=−16(x−2)2 −11
f(x)=−16(x−2)2 −11
f(x)=−16(x−2)2+69
f of x is equal to negative 16 times open paren x minus 2 close paren squared plus 69
f(x)=−16(x−2)2−59
f(x) = -16(x-2)^2 + 69
f of x is equal to negative 16 times open paren x minus 2 close paren squared plus 69