Question

The graph of a function is a parabola that has a minimum at (-1,-2) and goes through the point (0,1).

Answer 1

Answer:

$f(x) = 3 x^{2} + 6x +1$

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:

$f(x) = a (x-xvertex)^{2} + yvertex = a (x- -1)^2 + (-2) = a (x+1)^2 - 2$

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:

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

Answer 2

Answer:

f(x)=3x²+6x+1

Step-by-step explanation:

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