Answer:
1) Direction of opening: upward
2) Vertex is the point (-2,1)
3) Axis of Symmetry: x=-2
4) y-intercept: point (0,5)
5) Buddy point:
and

Explanation:
we have

This is the equation of a vertical parabola in vertex form
The general equation of a vertical parabola in vertex form is equal to

where
(h,k) is the vertex
a is the coefficient of variable x^2
If a > 0 -----> the parabola open upward and the vertex is a minimum
If a < 0 -----> the parabola open downward and the vertex is a maximum
The axis of symmetry is equal to the x-coordinate of the vertex
x=h
In this problem we have

The vertex is the point (-2,1)
The coefficient a is equal to a=1
so
a> 0
the parabola open upward and the vertex is a minimum
The axis of symmetry is
x=-2
Find out the y-intercept
Remember that the y-intercept is the value of y when the value of x is equal to zero
For x=0


The y-intercept is the point (0,5)
Find the x-intercepts
Remember that the x-intercept is the value of x when the value of y is equal to zero
so
For f(x)=0


The roots are complex
take square root both sides

Remember that


The solutions are


therefore
1) Direction of opening: upward
2) Vertex is the point (-2,1)
3) Axis of Symmetry: x=-2
4) y-intercept: point (0,5)
5) Buddy point:
and
