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