The equation of a parabola in vertex form, is:
Where <em>(h,k)</em> are the coordinates of the vertex.
From the given graph, notice that the coordinates of the vertex are:
The roots are the values of <em>x</em> where the graph crosses the x-axis. In this case, the graph crosses the x-axis at the points <em>(4,0)</em> and <em>(6,0).</em> Then, the roots are:
Substitute the values of the vertex into the equation of the parabola in vertex form:
To find the value of <em>a</em>, substitute <em>(x,y)=(4,0)</em>:
Therefore, the equation of the parabola is: