Question

John is organizing a local event. He expects the approximate attendance for the event to be modeled by the function a(t) = -16t2 + 48t + 64, where t is time in hours.

Assuming the event ends when there are no attendees, plot the domain to represent the duration of the event.
number line
< -5 -4 -3 -2 -1 0 1 2 3 4 5 >

Answer 1

The duration of this event is 4 hours

This function is a quadratic one

let Δ be the discriminant :

a = -16

b = 48

c= 64

Δ = 48²-4*(-16)*64 = 6400

So there are two values that satisfy -16t²+48t+64 = 0  x and y

x= (-48+80)/-16*2 = -1

y= (-48-80)/-16*2= 4

x<0 so w won't take it since time is a positive value here

so t = y = 4h

What is a quadratic equation meaning?

• Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation $x^2$+ 4x + 4 = 0.
• A quadratic problem is a type of problem in mathematics that deals with a variable multiplied by itself — an operation known as squaring. The area of a square is defined as its side length multiplied by itself in this language. The term "quadratic" is derived from the Latin word quadratum, which means "square."

Learn more about quadratic equation here:https://brainly.com/question/1214333

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