Which function has two x-intercepts, one at (0, 0) and one at (4, 0)?
f(x) = x(x - 4)
f(x) = x(x + 4)
f(x) = (x - 4)(x - 4)
f(x) = (x + 4)(x + 4)

Solution:

The intercepts can be identified by equating each of f(x) in the given options to zero.

(i) f(x) = x(x - 4)

Let f(x) = 0

x (x - 4) = 0

⇒ x = 0, x = 4

This has x-intercept at (0, 0) and (4, 0).

(ii) f(x) = x(x + 4)

Let f(x) = 0

x (x + 4) = 0

⇒ x = 0, x = -4

This has x-intercept at (0, 0) but not (4, 0).

(iii) f(x) = (x - 4)(x - 4)

Let f(x) = 0

(x - 4)(x - 4) = 0

⇒ x = 4

This has x-intercept at (4, 0) but not (0, 0).

(iv) f(x) = (x + 4)(x + 4)

Let f(x) = 0

(x + 4)(x + 4) = 0

x = -4

This does not have x-intercept at (0, 0) and (4, 0).

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Which function has two x-intercepts, one at (0, 0) and one at (4, 0)?

Summary:

f(x) = x(x - 4) has two x-intercepts, one at (0, 0) and one at (4, 0).