Question

If the equation y = (x - 6)(x + 12) is graphed in the xy-plane, what is the x-coordinate of the parabola’s vertex? Also please show the steps. :)

Answer 1

x- coordinate of vertex = - 3

the vertex lies on the axis of symmetry , which is positioned at the midpoint of the zeros

find the zeros by setting y = 0

(x - 6)(x + 12) = 0 ( equate each factor to zero and solve for x )

x - 6 = 0 ⇒ x = 6

x + 12 = 0 ⇒ x = - 12

x coordinate of vertex =
`(- 12+6)/(2)` =
`(-6)/(2)` = - 3