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)=16(x+1/2 )(x-1/2 )
⇕
h(x)= 16(x-( -1/2 ) )(x- 1/2 )
We can see that a= 16, p= - 12, and q= 12. Therefore, the x-intercepts occur at ( - 12,0 ) and ( 12,0 ).
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p=- 12 and q= 12, the axis of symmetry of our parabola is halfway between (- 12,0 ) and ( 12,0 ).
x=p+q/2 ⇒ x=- 12+ 12/2=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 - 4. Therefore, the vertex is the point (0,- 4).
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 - 4. We can write the domain and range of the function using this information.
Domain:& All real numbers
Range:& y ≥ - 4
