The function ƒ is defined by ƒ(x) = (x + 3)(x + 1). the graph of ƒ in the xy-plane is a parabola. which interval contains the x-coordinate of the vertex of the graph of ƒ?

All the intervals that contain the number are solution of the problem

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

where

(h,k) is the vertex of the parabola

In this problem we have

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

-------> equation in vertex form

The vertex is the point

The x-coordinate of the vertex is

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer: it's d

step-by-step explanation: