Question

A bird drops a stick from the top of Miami Tower. The height of the stick after x seconds is given by f(x) = 625 - 16x^2.

What is the maximum value of f(x)?

Answer 1

ANSWER

The maximum value is 625

EXPLANATION

The height of the stick that the bird dropped is modeled by the function;

$f(x) = 625 - 16x^2$

This function is already in the vertex form.

Let me rewrite it clearly for you to see.

$f(x) = - 16(x - 0)^2 + 625$

When we compare this to;

$f(x)=a(x-h)^2+k$

we have h=0 and k=625.

k=625 is the y-value of the vertex.

This is the maximum value on the graph of this function.

Answer 2

A function assigns the values. The maximum value of f(x) will be 625 units.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

As per the given question, the bird drops the sticks downwards, therefore, the height of the stick will be maximum, just after the bird leaves the stick. Therefore, when the time x=0. Thus, the maximum value of f(x) will be generated. Thus, the value of f(x) can be written as,

f(x)= -16x² + 625

f(0)= -16(0²) + 625

f(0) = 625

Hence, the maximum value of f(x) will be 625 units.

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