Question

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)

Answer 1

The answer is f(x)=x(x-4)

Answer 2

1. Consider the function y=f(x), the x-intercepts are the values of x for which f(x)=0

2. So an x-intercept has coordinates (x,0)

3. If (0, 0) is an x- intercept, then f(0)=0
If (4, 0) is an x- intercept, then f(4)=0

4. Check:

a. f(x) = x(x − 4)

f(0)=0(0-4)=0,
f(4)=4(4-4)=4*0=0

so f(x) = x(x − 4) has x intercepts at (0,0) and (4,0)

b. f(x) = x(x + 4)
f(0)=0*(0+4)=0 but f(4)=4(4+4)=4*8=32, so not 0

c. f(x) = (x − 4)(x − 4)
f(4)=(4-4)(4-4)=0
f(0)=(0-4)(0-4)=(-4)(-4)=16 so not 0

d. f(x) = (x + 4)(x + 4)
f(0)=(0+4)(0+4)=4*4=16 so not 0