A bullet is fired upward from ground level. Its height above the ground​ (in feet) at time t seconds is given by the following equation.
​H(t)equalsnegative 16 t squared plus 736 t
​(a) Find the vertex.
​(b) Find the time at which the bullet reaches its maximum height.
​(c) Find the maximum height.
​(d) Find the time at which the bullet hits the ground​ (when the height is equal to​ zero).

The given equation for the height \( H(t) \) of the bullet above the ground is:

\[
H(t) = -16t^2 + 736t
\]

This is a quadratic equation of the form \( H(t) = at^2 + bt + c \), where \( a = -16 \), \( b = 736 \), and \( c = 0 \) (since there is no constant term).

### (a) Find the Vertex:
The vertex of a parabola represented by \( H(t) = at^2 + bt + c \) occurs at \( t = -\frac{b}{2a} \).

Using the values of \( a = -16

A bullet is fired upward from ground level. Its height above the ground (in feet) at time t seconds is given by the following equation: H(t) = -16t^2 + 736t. (a) Find the vertex. (b) Find the time at which the bullet reaches its maximum height. (c) Find the maximum height. (d) Find the time at which the bullet hits the ground (when the height is equal to zero).

Learn how to solve a real-world quadratic equation problem involving the height of a bullet fired upward. This problem covers key algebraic concepts such as finding the vertex, determining the time of maximum height, calculating the maximum height, and solving for when the bullet hits the ground. Suitable for students in Grades 9-12.

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Solution

(a) Find the Vertex:

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