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Identify the interval (s) where the function is positive. y=x²-5x-36

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Final answer:

The interval where the function y = x² - 5x - 36 is positive is (-∞, -4) ∪ (9, ∞).

Step-by-step explanation:

To identify the interval(s) where the function y = x² - 5x -36 is positive, we need to determine the values of x for which the function's output, y, is greater than zero.

To do this, we can set up a sign chart. First, let's factor the quadratic equation: y = (x - 9)(x + 4).

We can see that the function is positive when x is greater than 9, or when x is less than -4. Therefore, the interval where the function is positive is (-∞, -4) ∪ (9, ∞).

User Ovidiu Unguru
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