The vertex of the parabola below is at the point (-2, -1), and the point (-1, 1) is on the parabola. Write the equation of the parabola.

  y = 2(x +2)^2 -1

Step-by-step explanation:

The vertex form of the equation of a parabola is ...

  y = a(x -h)^2 +k . . . . . vertex (h, k), scale factor "a"

We know the vertex, so we can find the scale factor from the other point.

  1 = a(-1+2)^2 -1 = a -1

  2 = a . . . . . . add 1

The equation of the parabola is ...

  y = 2(x +2)^2 -1

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.