To graph the equation
The standard form is already given as
Step 1: Find the Vertex
The vertex of a parabola given in the form
Here,
To find the y-coordinate of the vertex, substitute
So, the vertex is at the point
Step 2: Finding the Roots
To find the roots of the equation
Rearranging gives:
Now we can either factor or use the quadratic formula:
Here,
Calculating the two roots:
Step 3: Identify Points on the Graph
Now we have the following important points:
- Vertex:
- Roots:
and
Step 4: Choose Additional Points
Let's choose two more points to fully represent the graph. We can evaluate the function at
- For
:
- For
:
Summary of Points to Graph
The points to plot are:
- Vertex: (-5, 1)
- Root 1: (-4, 0)
- Root 2: (-6, 0)
- Point: (-7, -3)
- Point: (-3, -3)
Step 5: Graphing
You can plot these points on a Cartesian coordinate system. The parabola opens downward with roots at (-4, 0) and (-6, 0) and a vertex at (-5, 1).
Conclusion
The roots of the equation