Function notation for an equation w/ 1 side equal to the greater of two expressions

Hello. Thank you in advance for any help you can offer. I'm working with afunction that relates flow and pressure. For simplicity, let’s say the function is P = A Q^2, where P is pressure, Q is flow, and A isconstant. This equation accuratelydescribes the behavior of a system when Q exceeds a certain value. Below this threshold, P is constant. For the systems I am now contemplating, Iknow what the threshold value of P is, but I don’t yet know A. So, right now, I don’t know the value of Qthat corresponds to the known pressure threshold.
Let’s say that Iknow that P can never be less than 80 and through experiments I learn that A = 5. In this case, I’ll be able write: P = 80 when Q < 4; P = 5 Q^2 when Q > = 4. While this notation may not comply withapplicable math notation standards, a reader would probably get the gist of what I’mtrying to say. (By the way, I would liketo know the technically correct way to express this conditional if somebodywould kindly show me.)
More immediately, I would liketo better understand the correct way to express the above equation when I don’t yetknow A and the value of Q that corresponds to the known minimum threshold ofP. For example: I want to write an expressionthat says P is equal to the greater of these two values: 80 or A Q^2. What is the correct notation to express this?
Thanks!

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Originally Posted by Wayintense

Hello. Thank you in advance for any help you can offer. I'm working with afunction that relates flow and pressure. For simplicity, let’s say the function is P = A Q^2, where P is pressure, Q is flow, and A isconstant. This equation accuratelydescribes the behavior of a system when Q exceeds a certain value. Below this threshold, P is constant. For the systems I am now contemplating, Iknow what the threshold value of P is, but I don’t yet know A. So, right now, I don’t know the value of Qthat corresponds to the known pressure threshold.
Let’s say that Iknow that P can never be less than 80 and through experiments I learn that A = 5. In this case, I’ll be able write: P = 80 when Q < 4; P = 5 Q^2 when Q > = 4. While this notation may not comply withapplicable math notation standards, a reader would probably get the gist of what I’mtrying to say. (By the way, I would liketo know the technically correct way to express this conditional if somebodywould kindly show me.)
More immediately, I would liketo better understand the correct way to express the above equation when I don’t yetknow A and the value of Q that corresponds to the known minimum threshold ofP. For example: I want to write an expressionthat says P is equal to the greater of these two values: 80 or A Q^2. What is the correct notation to express this?
Thanks!

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Simple. $\displaystyle P = max(80, AQ^2)$

-Dan

Thank you Dan! Simple, elegant, and (sadly) completely out of mind until you pointed me in the right direction! Thanks again.