a) h = 12 ft, b) h = - 0.5 · (d - 6) · (d + 4), c) d₁ = 6, d₂ = -4, d) 6 ft, e) Please see the image attached below for further details.
How to analyze a second order polynomial related to the trajectory of the rock under parabolical motion
An object is under a parabolical motion, when it has a horizontal motion at constant velocity and a vertical motion uniformly accelerated by gravity and effects from air viscosity are neglected. In this case, the trajectory is described by second order polynomial (quadratic function).
a) The height of the cliff is found by evaluating the function at d = 0:
h = - 0.5 · 0² + 0 + 12
h = 12 ft
The initial height of the cliff is 12 feet. [tex]\blacksquare[/tex]
b) The intercept form of the quadratic function is found by algebraic procedures:
h = - 0.5 · d² + d + 12
h = - 0.5 · (d² - 2 · d - 24)
h = - 0.5 · (d - 6) · (d + 4)
The relation in intercept form is h = - 0.5 · (d - 6) · (d + 4). [tex]\blacksquare[/tex]
c) The zeros of the relation are d₁ = 6 and d₂ = -4. [tex]\blacksquare[/tex]
d) The rock hit the ground at a horizontal distance of 6 feet. [tex]\blacksquare[/tex]
e) The relation is graphed below. [tex]\blacksquare[/tex]
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