On a coordinate plane, a parabola opens up. it goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
which describes all of the values for which the graph is positive and decreasing?

all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3

Option A.

Step-by-step explanation:

It is given that an open up parabola goes through (-1, 0), has a vertex at (1, -4), and goes through (3, 0).

x-intercepts of the function are (-1,0) and (3,0).

The vertex of an upward parabola is the point of minima. The function is decreasing on the left side of the vertex and the function is increasing on the right side of the vertex. It means

Function is positive and decreasing where x<-1

Function is negative and decreasing where -1 < x < 1.

Function is negative and increasing where 1 < x < 3.

Function is positive and increasing where x>3.

Therefore, the correct option is A.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.