How do you find the vertex of #y= (x-3)(x+3)#?
2 Answers
Construct the vertex using part geometry and part algebra to find
Explanation:
This is a vertical parabola that cuts the
Since parabolas are symmetrical, its axis must be midway between these, namely the vertical line
The axis intersects the parabola at the vertex, so substitute
that is the point
graph{(x-3)(x+3) [-19.91, 20.09, -12.08, 7.92]}
Multiply out to find
giving
Explanation:
(use the difference of squares identity:
So
This takes minimum value when
When
So the vertex is at