Question

(HELP PLEASE) Select all of the statements that can be determined from the table given.



A. There is a y-intercept at (-4,0).

B. There are x-intercepts at (-1,0) and (4,0).

C. There is a line of symmetry at x=1.5

D. In the interval from x=0 to x=5, F(x) is increasing.

Answer 1

B, C are your answers. The other two are false. Vertex is at x = 1.5 y = -7

Answer 2

Answer:

B. There are x-intercepts at $(-1,0)$ and $(4,0)$

C. There is a line of symmetry at $x=1.5$

Step-by-step explanation:

we know that

The x-intercepts are the values of x when the value of the function is equal to zero

The y-intercepts are the values of y when the value of x is equal to zero

Observing the table

The  x-intercepts are the points $(-1,0)$ and $(4,0)$

The  y-intercept is the point $(0,-4)$

Plot the points

The axis of symmetry is $x=1.5$ ----> the x-coordinate of the vertex is $1.5$

The function is increasing in the interval-----> (1.5,∞)

The function is decreasing in the interval-----> (-∞, 1.5)

therefore

Statements

B. There are x-intercepts at $(-1,0)$ and $(4,0)$

The statement is True

C. There is a line of symmetry at $x=1.5$

The statement is True --------> see the attached figure