The function
d(t)=-2t^2+7t+4
most closely represents the height(h) of the golf ball in feet after t seconds. How high does the golf ball reach?
the max occurs on the axis of symmetry of the parabola
tmax = -b / 2a = -7 / (2 * -2)
substitute tmax back into d(t) to find dmax
d(t)=-2t^2+7t+4
To determine the height at which the golf ball reaches, we need to find the vertex of the function, as the vertex represents the maximum or minimum point of a quadratic function.
Given the function: d(t) = -2t^2 + 7t + 4
We can determine the vertex using the formula: t = -b / (2a), where a, b, and c are coefficients of the quadratic equation in standard form (ax^2 + bx + c).
In this case, a = -2 and b = 7.
So, t = -7 / (2 * -2)
= -7 / -4
= 7/4
= 1.75
Now, to find the height(h) corresponding to this time (t), we substitute t = 1.75 back into the function:
d(1.75) = -2(1.75)^2 + 7(1.75) + 4
= -2(3.0625) + 12.25 + 4
= -6.125 + 12.25 + 4
= 10.125
Therefore, the golf ball reaches a height of 10.125 feet.