Question

The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x – 4) represents the image. At which points does the image cross the x-axis?

Answer 1

A (-8, 0) and (4, 0)

Answer 2

x = -8 and x = 4

Explanation:

given

f(x) = (x+8) (x - 4)

recall that at any point on the x-axis, y = 0 [i.e f(x) = 0]

hence to find where the graph crosses the x-axis, we simply substitue f(x) = 0 into the equation and solve for x

f(x) = (x+8) (x - 4)

0 = (x+8) (x - 4)

Hence

either,

(x+8) = 0 ----> x = -8 (first crossing point)

or

(x-4) = 0 ------> x = 4 (second crossing point)

Hence the graph crosses the x-axis at x = -8 and x = 4