Welcome to the article The function tex h 16t 2 128t tex represents the height h in feet of a firework t seconds after it is launched The firework. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Final answer:
The firework, represented by the function h=-16t²+128t, explodes at its highest point, which is 4 seconds after being launched.
Explanation:
The question mentions a quadratic function, h=-16t²+128t, which represents the height of a firework launched. The highest point (or the vertex of the parabola represented by this function) is when the firework explodes. To find this, we should set the derivative of the function to zero.
By finding the derivative of the function, we get -32t + 128. Setting this to zero gives us t = 4. This means that the firework explodes at t = 4 seconds.
It's also important to note that in the context of this problem, negatives and values greater than the lifespan of the firework are meaningless and can be excluded. Thus, we're only interested in positive time values. The firework thus explodes 4 seconds after being launched.
Learn more about Quadratic Functions here:
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Rewritten by : Brahmana