f(x)=a(x-p)(x-q)
In this form, where a ≠0, the x-intercepts are p and q. Let's consider the intercept form of our function.
f(x)=(x+2)(x-6)
⇕
f(x)= 1(x-( - 2))(x- 6)
We can see that a= 1, p= -2, and q= 6. Therefore, the x-intercepts occur at ( -2,0) and ( 6,0).
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p=-2 and q=6, the axis of symmetry of our parabola is halfway between (-2,0) and (6,0).
x=p+q/2 ⇒ x=-2+ 6/2=4/2=2
We found that the axis of symmetry is the vertical line x=2.
Find and Plot the Vertex
Since the vertex lies on the axis of symmetry, its x-coordinate is 2. To find the y-coordinate, we will substitute 2 for x in the given equation.
