Question

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.

Answer 1

f(x)=3x²+6x+1

Explanation:

#PLATOFAMILY

Answer 2

`f(x) = 3 x^(2) + 6x +1`

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:

`f(x) = a (x-xvertex)^(2) + yvertex = a (x- -1)^2 + (-2) = a (x+1)^2 - 2`

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:

`f(0) =  a (0+1)^2 -2 = 1`

which gives us:
`a (1) -2 =1` therefore,
`a = 3`

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

`f(x) = 3 (x+1)^2 -2`

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

`f(x) = 3 (x^2 +2x+1) -2 = 3x^2 +6x +3 -2 = 3x^2 +6x +1`