Recall the intercept form of a quadratic function.
h(x)=-(x+2)(x-7)
In this form, where a ≠0, the x-intercepts are p and q. Let's consider the intercept form of our function.
h(x)=-(x+2)(x-7)
⇕
h(x)=( -1)(x-( -2))(x- 7)
We can see that a= -1, p= - 2, and q= 7. Therefore, the x-intercepts occur at ( -2 ,0) and ( 7,0).
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p= -2 and q= 7, the axis of symmetry of our parabola is halfway between (-2,0) and (7,0).
x=p+ q/2 ⇒ x=( -2)+ 7/2=2.5
We found that the axis of symmetry is the vertical line x=2.5.
Find and Plot the Vertex
Since the vertex lies on the axis of symmetry, its x-coordinate is 2.5. To find the y-coordinate, we will substitute 2.5 for x in the given equation.
