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Chapter 6: Q47. (page 292)

An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by h(t)=-16t2+80t+200. Interpret the meaning of the y-intercept in the context of this problem.

Short Answer

Expert verified

The meaning of y-intercept is the height from which the object is fired at 0 seconds.

Step by step solution

01

Step 1. Given Information.

The given function is h(t)=-16t2+80t+200

02

Step 2. Use the concept.

The y-intercept is the point where the graph intersects they-axis.

Consider the function f(x)=ax2+bx+c,a鈮�0, the x-coordinate of vertex is -b2a.

The Graph of f(x)=ax2+bx+c,a鈮�0

  • opens up and has a minimum value when a>0, and
  • opens down and has a maximum value when a<0
03

Step 3. Solution.

In the function h(t)=-16t2+80t+200, we have a=-16,b=80,c=200

So, the y-intercept is given by substituting t=0

鈬�h(0)=-1602+800+200=200

Which is the height from which the object is fired initially.

So, the meaning of y-intercept is the height from which the object is fired at 0 seconds.

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