The equation h=-16t^2+58t+3 models the height of a baseball t seconds after it has been hit.
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The value of such that the line
is tangent to the parabola
is
.
If is a line <em>tangent</em> to the parabola
, then we must observe the following condition, that is, the slope of the line is equal to the <em>first</em> derivative of the parabola:
(1)
Then, we have the following system of equations:
(1)
(2)
(3)
Whose solution is shown below:
By (3):
(3) in (2):
(4)
(4) in (1):
The value of such that the line
is tangent to the parabola
is
.
We kindly invite to check this question on tangent lines: brainly.com/question/13424370
Since the lines are parallel and you know the slope of 
is -2, you know the slope of line 
will also be -2. You can see on the coordinate grid that line crosses the y-axis at -1. When you piece all of these facts together into slope-intercept form you get = -2x - 1.