Question

A couple of students are testing a prototype for a science project on rockets. They launch the rocket and record its height over time. The table shows the height of the rocket in meters, f(x), and the time in seconds after launch, x. Create the function, in standard form, that models this situation.

Answer 1

For this case we have the following table:
 x    f(x)
 0     2
 1     5
 2    10
 3     17
 The equation that best fits the data in the table, for this case, is given by a quadratic function.
 The quadratic function in its standard form is:
 f (x) = x2 + 2x + 2
 Answer:
 f (x) = x2 + 2x + 2

Answer 2

Answer:

Substitute b = 2 in the equation 3 = a + b and solve to get a = 1.

Substitute the values of a = 1, b = 2, and c = 2 in the standard form of the quadratic function:

f(x) = x^2 + 2x + 2

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