Answer:
Vertex: , Axis of symmetry: , no x-Intercepts, y-Intercepts: . The graph is represented in the image attached below.
Step-by-step explanation:
The equation of the parabola in vertex form and whose axis of symmetry is vertical is described by this formula:
(1)
Where:
- Independent variable.
- Dependent variable.
- Vertex constant.
- Coordinates of the vertex.
By direct comparison, we find the following information:
, ,
Vertex
The vertex is a point of the parabola so that .
If we know that and , then the coordinates of the vertex are .
Axis of symmetry
The axis of symmetry is a line of the form .
If we know that , then the axis of symmetry is .
To find the x and y intercepts, we need to transform the equation of the parabola into its standards, which is a second grade polynomial:
If we know that , and , then the equation of the parabola in standard form is:
x-Intercepts
The x-intercepts of the polynomial (if exist) can be found by the Quadratic Formula:
As both roots are conjugated complex numbers, there are no x-intercepts.
y-Intercepts
The y-intercept (if exists) can be found by evaluating the polynomial at :
The y-intercept is .
Lastly, we proceed to plot the function by using graphing tools.