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 find the x-intercepts of the function \( f(x) = 2x^2 - 2x \), we need to set the function equal to zero and solve for \( x \):

\[ f(x) = 0 \]

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

Factoring out the common term:

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

Setting each factor to zero gives us:

1. \( 2x = 0 \) → \( x = 0 \)
2. \( x - 1 = 0 \) → \( x = 1 \)

So, the x-intercepts are at the points \( (0, 0) \) and \( (1, 0) \).

Thus, the statement "The x-intercepts of this graph are (0,0) and (1,0)" is true.