Acouple 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.

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
 
 f (x) = x2 + 2x + 2

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12