Question
Graph the function f(x)=2x^2−2x
. True or false: The x-intercepts of this graph are (0,0)and (1,0)
. True or false: The x-intercepts of this graph are (0,0)and (1,0)
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Answered by
GPT-4o mini
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 \( (1,0) \).
\[
2x^2 - 2x = 0
\]
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 \( (1,0) \).
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