The graph of a function is a parabola that has a minimum at (-1,-2) and goes through the point (0,1).
what is the equation of the function in standard form?
substitute numerical values for a, b, and c.

Step-by-step explanation:

Since they give us the coordinates of the minimum of the parabola (the parabola's vertex), we start by writing the function in vertex form:

Now we use the fact that the point (0,1) is on the graph of the parabola, which means that when x=0, the value of the function (y) must be equal to 1.

We apply this to the expression we found above:

which gives us:    therefore,

Now we write the function using the value of the constant a we just found:

and next we find the square of the binomial (x+1) to express the function in standard form:

4

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet