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Created with Fabric.js 1.4.5 start from scratch[clears the canvas] The bullet hits the ground 6 seconds after the shot is fired. To mathematically solve for this part of the problem,I used the following steps:0= -4.9t^2 + 19.6t + 58.80= -4.9(t^2 - 4t - 12)0= -4.9(t-6)(t+2). The zeros (x-intercepts) are 6 and -2 because you take the opposite of the number in the finalparentheses. Since a bullet could not land on the ground at -2 seconds, this is not a reasonable answer in relation to this problem. Therefore, the only logical solution for this problem is the x-intercept of 6. This means the bullet hit the ground after 6 seconds. Shooting Power X-intercept X-intercept Y-intercept Vertex/Maximum A gun is shot upwards into the air from the top of abuilding that is 58.8 yards tall. The bullet is travelling at a speed of 19.6 yards per second. The equation for the bullet's height (h) at a set time (t)after it was fired from the gun is h(t)=-4.9t^2 + 19.6t + 58.8. Calculating the Zeros/X-Interceptsand Their Meanings Calculating the Y-Interceptand its Meaning The y-intercept for this problem is 58.8. To calculate this important piece of information, you simply put 0 in for the time in the original equation since time is 0 when finding the y-intercept.h(t) = -4.9t^2 + 19.6t + 58.8h(0) = -4.9 (0)^2 + 19.6(0) + 58.8h(0) = 58.8The y-intercept in this problem shows the height fromwhich the bullet was fired. Calculating the Vertex/Maximum and its Meaning The vertex (maximum) for this problem is (2, 78.4). To calculate this, you would perform the followingmathematical steps:h(t) = -4.9t^2 + 19.6t + 58.8a = -4.9, b = 19.6, c = 58.8Finding the x value of the Vertex: x = -b/(2a)x = -19.6/(2 x -4.9)x = -19.6/-9.8x = 2To find the y value of the vertex, substitute 2 in for t (time) in the problem's original equation.h(2) = -4.9(2)^2 + 19.6(2) + 58.8h(2) = 78.4This means that the maximum height that the bullet will reach will be 78.4 yards. It will reach this maximum height 2 seconds after the gun has beenfired.
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