Recall the intercept form of a quadratic function.
h(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)=- 5x(x-1)
⇕
h(x)= - 5(x- 0)(x- 1)
We can see that a= -5, p= 0, and q= 1. Therefore, the x-intercepts occur at ( 0,0) and ( 1,0).
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p=0 and q=1, the axis of symmetry of our parabola is halfway between (0,0) and (1,0).
x=p+q/2 ⇒ x=0+ 1/2=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 54. Therefore, the vertex is the point ( 12, 54).
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 54. We can write the domain and range of the function using this information.
Domain:& all real numbers
Range:& y ≤ 5/4
