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