Answer and Explanation :
Given : Function
To find : The vertex, axis of symmetry, maximum or minimum value, and the graph of the function.
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,
Refer the attached figure below.