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- 1)(x- 8)
We can see that a= 4, p= 1, and q= 8. Therefore, the x-intercepts occur at ( 1,0) and ( 8,0).
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p= 1 and q= 8, the axis of symmetry of our parabola is halfway between (1,0) and (8,0).
x=p+ q/2 ⇒ x=1+ 8/2=9/2
We found that the axis of symmetry is the vertical line x= 92.
Find and Plot the Vertex
Since the vertex lies on the axis of symmetry, its x-coordinate is 92. To find the y-coordinate, we will substitute 92 for x in the given equation.
The y-coordinate of the vertex is - 49. Therefore, the vertex is the point ( 92,- 49).
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 - 49. We can write the domain and range of the function using this information.
Domain:& All real numbers
Range:& y ≥ - 49
