Graph the function f(x)=2x2−2x . True or false: The x-intercepts of this graph are (0,0) and (1,0) .

Question

Type 1 for true.

Type 2 for false.

(1 point)

Answer 1

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

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

We can factor this equation:

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

Setting each factor equal to zero gives us the solutions:

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

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

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

Type 1 for true.