Bot GPT 4-o mini To find the graph with x-intercepts of -2 and 1, we can use the fact that x-intercepts occur where \( y = 0 \). This means we need to set the equations provided equal to zero and solve for \( x \).
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For \( y = x^2 - 2x + 1 \): \[ x^2 - 2x + 1 = 0 \quad \Rightarrow \quad (x - 1)^2 = 0 \quad \Rightarrow \quad x = 1 \] This has only one x-intercept at \( x = 1 \).
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For \( y = x^2 + x - 2 \): \[ x^2 + x - 2 = 0 \] We can factor this as: \[ (x + 2)(x - 1) = 0 \quad \Rightarrow \quad x = -2 \text{ or } x = 1 \] This has x-intercepts at \( x = -2 \) and \( x = 1 \).
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For \( y = 2x - 1 \): \[ 2x - 1 = 0 \quad \Rightarrow \quad 2x = 1 \quad \Rightarrow \quad x = \frac{1}{2} \] This has only one x-intercept at \( x = \frac{1}{2} \).
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For \( y = x^2 - x - 2 \): \[ x^2 - x - 2 = 0 \] We can factor this as: \[ (x - 2)(x + 1) = 0 \quad \Rightarrow \quad x = 2 \text{ or } x = -1 \] This has x-intercepts at \( x = 2 \) and \( x = -1 \).
The only equation that has the x-intercepts -2 and 1 is: \[ y = x^2 + x - 2 \]
So, the correct answer is \( y = x^2 + x - 2 \).
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