In this form, where a ≠0, the x-intercepts are p and q. Let's consider the intercept form of our function.
f(x)=-2(x+9)(x-3)
⇕
f(x)= -2(x-( - 9))(x- 3)
We can see that a= -2, p= - 9, and q= 3. Therefore, the x-intercepts occur at ( -9,0) and ( 3,0).
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p= -9 and q= 3, the axis of symmetry of our parabola is halfway between (-9,0) and (3,0).
x=p+ q/2 ⇒ x=-9+ 3/2=-3
We found that the axis of symmetry is the vertical line x=-3.
Find and Plot the Vertex
Since the vertex lies on the axis of symmetry, its x-coordinate is -3. To find the y-coordinate, we will substitute - 3 for x in the given equation.
