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Consider the graph of the function y=x squared + 2x-8 For each statement in the table, determine whether it is true or false.
The y-intercept of the function is located at [0,-8]
An x-intercept of the function is located at [-4,0]
An x-intercept of the function is located at [-2,0]
The minimum of the function is located at [0,-8]
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GPT-5 mini
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y = x^2 + 2x − 8
1. The y-intercept is at [0, −8]. — True. Plug x = 0 → y = −8.
2. An x-intercept is at [−4, 0]. — True. x^2 + 2x − 8 = (x + 4)(x − 2), so x = −4 is a root.
3. An x-intercept is at [−2, 0]. — False. The roots are x = −4 and x = 2, not −2.
4. The minimum is at [0, −8]. — False. Vertex is at x = −b/(2a) = −1, y = (−1)^2 + 2(−1) − 8 = −9, so the minimum is at [−1, −9].
1. The y-intercept is at [0, −8]. — True. Plug x = 0 → y = −8.
2. An x-intercept is at [−4, 0]. — True. x^2 + 2x − 8 = (x + 4)(x − 2), so x = −4 is a root.
3. An x-intercept is at [−2, 0]. — False. The roots are x = −4 and x = 2, not −2.
4. The minimum is at [0, −8]. — False. Vertex is at x = −b/(2a) = −1, y = (−1)^2 + 2(−1) − 8 = −9, so the minimum is at [−1, −9].
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