The values in the table represent the graph of a continuous function. which interval must contain an x-intercept?
x y
–3.1 –1.85
–2.7 –0.84
–2.3 –0.09
–1.9 0.44
–1.5 0.79
–1.1 1.00
–0.7 1.10
–0.3 1.13
0.1 1.13
a. –3.1 < x < –2.7
b. –2.3 < x < –1.9
c. –1.5 < x < –1.1
d. –0.3 < x < 0.1

B. –2.3 < x < –1.9

Step-by-step explanation:

The x-intercept is where the line crosses through the x-axis. At the x-intercept, the y values of the function increase and change from negative to positive. This happens in the table between x = -2.3 and x = -1.9. The interval is B. –2.3 < x < –1.9.

option: B is the correct answer.

                B. –2.3 < x < –1.9

We know that an x-intercept of a graph is a point where the y-value is zero.

i.e. it is an ordered pair where the y-value is zero.

We are given  a table of values as:

      X           Y

    –3.1     –1.85

    –2.7    –0.84

    –2.3    –0.09

    –1.9      0.44

    –1.5      0.79

    –1.1       1.00

    –0.7      1.10

    –0.3      1.13

       0.1      1.13

Here we see that the y-value is increasing from negative to positive.

Hence, it will intersect the x-axis at a point.

The interval where we will get an x-intercept is:

                B. –2.3 < x < –1.9

Since at x= -2.3 we have:  y= -0.09

and at x= -1.9 we have:  y= -.44

i.e. in this interval the graph will cut the x-axis.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

d is the answer

step-by-step explanation: