To draw the graph of the given function, we will follow four steps.
- Identify and plot the .
- Find and graph the .
- Find and plot the .
- Draw the through the vertex and the points where the intercepts occur.
Let's go through these steps one at a time.
Identify and Plot the intercepts
Recall the of a quadratic function.
In this form, where the intercepts are and Let's consider the factored form of our function.
We can see that and Therefore, the intercepts occur at and
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between and Since we know that and the axis of symmetry of our parabola is halfway between and
We found that the axis of symmetry is the
Find and Plot the Vertex
Since the vertex lies on the axis of symmetry, its
To find the
coordinate, we will substitute
in the given equation.
coordinate of the vertex is
Therefore, the vertex is the point
Draw the Parabola
Finally, we will draw the parabola through the vertex and the intercepts.