What is the vertex form, f(x) = a(x − h)^2 + k, for a parabola that passes through the point (1, −7) and has (2, 3) as its vertex. What is the standard form of the equation?

A) Vertex form: f(x) = 10(x + 4)^2 + 5
Standard form: f(x) = −10x^2 + 40x + 165

B) Vertex form: f(x) = −6(x − 4)^2 + 3
Standard form: f(x) = −6x^2 + 7x − 24

C) Vertex form: f(x) = −10(x − 2)^2 + 3
Standard form: f(x) = −10x^2 + 40x − 37

D) Vertex form: f(x) = −3(x − 2)^2 + 4
Standard form: f(x) = −3x^2 + 12x +16

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)