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

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

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

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