In this form, where a ≠0, the x-intercepts are p and q. Let's consider the intercept form of our function.
y=3(x-5)(x+5)
⇕
y= 3(x- 5)(x-( -5))
We can see that a= 3, p= 5, and q= -5. Therefore, the x-intercepts occur at ( 5,0) and ( -5,0).
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p= 5 and q= - 5, the axis of symmetry of our parabola is halfway between (5,0) and (-5,0).
x=p+ q/2 ⇒ x=5+( -5)/2=0
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 0 for x in the given equation.
