A fisherman is holding a fishing rod .5m above the water. The fishing rod reaches its maximum height 1.5m above and 1m to the left of his hand. Determine the quadratic function that describes the arc of the fishing rod.
If we say that the origin (0,0) is his hand, then the maximum of the arc is at (-1, 1.5).
An ‘arc’ means a negative quadratic.
It is shifted to the left by 1 from the origin.
Its max is 1.5, so we add 1.5
-(x+1)^2 + 1.5
= -x^2 - 2x + 0.5
Check if this is true:
x = -b / 2a
y = ax^2 + bx + c
a = -1, b = -2, c = 0.5
-b/2a = - (-2)/2(-1)
y(-1) = - (-1)^2 - 2(-1) + 0.5
y(-1) = 1.5
This confirms that
-x^2 - 2x + 0.5 is correct, assuming the fisherman’s hand is at the origin.
Now, how this relates to the .5m that his hand is above the water is unclear because your question doesn’t specifically state the frame of reference.
If the frame of reference is the water, then the graph is shifted up by .5m