Question 446122
If an object is tossed into the air the path of this object is represented by the
 equation atē+bt+c=h where h is the height after t seconds, a is the acceleration
 due to gravity, b is the initial velocity, and c is the initial height.
:
a.A rocket is thrust vertically upward from the top of a tower 80 feet tall,
 with an initial velocity of 64 ft/s, (the acceleration due to gravity is -16ft/sec).
 Write the quadratic equation representing this scenario when h is 0.
-16t^2 + 64t + 80 = 0
:
b.Find the roots (solutions) for this quadratic equation, solving by factoring.
-16t^2 + 64t + 80 = 0
Simplify, divide by -16, (makes it easier to factor), results:
t^2 - 4t - 5 = 0
factors to
(t-5)(t+1) = 0
Roots
t=+5
t=-1
:
c.How high will the rocket be after 3 seconds?
Replace t with 3 in the original equation
h = -16(3^2) + 64(3) + 80
h = -16(9) + 192 + 80
h = -144 + 192 + 80
h = 128 ft after 3 sec
:
d.How long will it take for the rocket to hit the ground?
the positive root: t=5 sec, then h=0, which is the ground
:
Given the graph of the equation, identify and appropriately label, the vertex, solutions or roots, all intercepts, and axis of symmetry.
{{{ graph( 300, 200, -2, 8, -20, 150, -16x^2+64x+80) }}}
You can see on the graph, the x intercepts, -1 and +5, y intercept y=80
Vertex: x=2, y=144  Axis of symmetry: x=2