Recall the intercept form of a quadratic function.
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.
h(x)=4(x+3)(x-3)
⇕
h(x)= 4(x-( - 3))(x- 3)
We can see that a= 4, p= -3, and q= 3. Therefore, the x-intercepts occur at ( -3,0) 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=-3 and q=3, the axis of symmetry of our parabola is halfway between (-3,0) and (3,0).
x=p+q/2 ⇒ x=-3+ 3/2=0/2=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.
The y-coordinate of the vertex is - 36. Therefore, the vertex is the point (0,- 36).
Draw the Parabola
Finally, we will draw the parabola through the vertex and the x-intercepts.
We can see above that there are no restrictions on the x-variable. Furthermore, the y-variable takes values greater than or equal to - 36. We can write the domain and range of the function using this information.
Domain:& all real numbers
Range:& y ≥ - 36
