For the function below, find the vertex, axis of symmetry, maximum or minimum value, and the graph of the function.

f(x)=(x^2/2) + 2x +1

Answer and Explanation :

Given : Function

To find : The vertex, axis of symmetry, maximum or minimum value, and the graph of the function.

Solution :

The quadratic function is in the form,

On comparing, , b=2 and c=1

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

For k, The y-coordinate of the vertex is given by,

The vertex of the function is (h,k)=(-2,-1)

The x-coordinate of the vertex i.e. is the axis of symmetry,

So, (solved above)

So, The axis of symmetry is x=-2.

The maximum or minimum point is determine by,

If a > 0 (positive), then the parabola opens upward and the graph has a minimum at its vertex.

so,  the parabola opens upward and the graph has a minimum at its vertex.

The Minimum value is given at (-2,-1)

Now, We plot the graph of the function

At different points,

x          y

-4        1

-2        -1

0         1

Refer the attached figure below.

it should be a and d. lmk if i'm wrong xd