Question

A function is shown: f(x) = 36x2 − 1.

Choose the equivalent function that best shows the x-intercepts on the graph.

f(x) = 18(x2 − 1)
f(x) = (18x + 1)(18x − 1)
f(x) = 6(x2 + 1)
f(x) = (6x + 1)(6x − 1)

Answer 1

D

Explanation:

f(x) = (6x+1)(6x-1)

Answer 2

The equivalent function:
`f(x)=(6x+1)(6x-1)`

Explanation:

The x-intercepts of the given function on the graph can be obtained by equating the function to zero.

This is because on the x-axis, the y-coordinate is zero.

`36x^(2) -1=0\\36x^(2) =1\\x=(1)/(6),-(1)/(6)`

The function that has the same x-intercepts on the graph from the given options is:

`f(x)=(6x+1)(6x-1)`

Alternate Method:

The answer can also be obtained by factorizing the question.