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

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step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for