Which function in vertex form is equivalent to f(x) = x2 + x +1? O f(x) = (x + 3+
1
3
o f(x)
4
f(x) = (x +
f(x) = (x + +
f(x) = (x + 3D + 1
IN

Step-by-step explanation:

We are given the function:

.

And we want to turn this into vertex form.

Note that our given function is in the standard form:

In other words, a = 1, b = 1, and c = 1.

To convert from standard form to vertex form, we can either: (1) complete the square, or (2) find the vertex manually.

In most cases, the second method is more time efficient.

Vertex form is given by:

Where a is the leading coefficient and (h, k) is the vertex.

We have already determined that a = 1.

Find the vertex. The x-coordinate of the vertex of a quadratic is given by:

Therefore, our point is:

To find the y-coordinate or k, substitute this value back into the function:

Thus, the vertex is (-1/2, 3/4). So, h = -1/2 and k = 3/4.

Hence, the vertex form is:

Simplify:

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step-by-step explanation:

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0