In this form, where a ≠0, the x-intercepts are p and q. Let's consider the intercept form of our function.
y=-2(x-3)(x+4) ⇔ y= - 2(x- 3)(x-( - 4))
We can see that a= -2, p= 3, and q= -4. Therefore, the x-intercepts occur at ( 3,0) and ( -4,0).
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=-4, the axis of symmetry of our parabola is halfway between (3,0) and (-4,0).
x=p+q/2 ⇒ x=3+( -4)/2=- 1/2
We found that the axis of symmetry is the vertical line x=- 12.
Find and Plot the Vertex
Since the vertex lies on the axis of symmetry, its x-coordinate is - 12. To find the y-coordinate, we will substitute - 12 for x in the given equation.
The y-coordinate of the vertex is 492. Therefore, the vertex is the point (- 12, 492).
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 less than or equal to 492. We can write the domain and range of the function using this information.
Domain:& All real numbers
Range:& y ≤ 49/2
