Question

Graph the function f(x)=2x^2−2x
. True or false: The x-intercepts of this graph are (0,0)and (1,0)

Answer 1

To determine whether the x-intercepts of the function \( f(x) = 2x^2 - 2x \) are \( (0,0) \) and \( (1,0) \), we need to find the points where the function equals zero, i.e., we solve the equation:

\[
2x^2 - 2x = 0
\]

We can factor this equation:

\[
2x(x - 1) = 0
\]

Setting each factor equal to zero gives us:

1. \( 2x = 0 \) which simplifies to \( x = 0 \)
2. \( x - 1 = 0 \) which simplifies to \( x = 1 \)

Thus, the x-intercepts are:

\[
(0, 0) \quad \text{and} \quad (1, 0)
\]

This means that the statement is **true**: the x-intercepts of the graph are indeed \( (0,0) \) and \( (1,0) \).