Question

Explain why a quadratic equation is used to model problems involving finding a maximum or minimum.

Answer 1

Look at the graph of a quadratic function, what do you notice?

Answer 2

could it be like for maximum how high an object went?

Answer 3

Okay, assuming you have to answer exactly what they ask you, then you should explain the reason why you can use a quadratic function to model a problem having a maximum or a minimum.
Now, if you have a quad. function you have (basically) two options:
For f(x)=ax^2+bx+c
If a>0

If a<0

According to what we can see there, we can almost inmediatly find the maximum (a<0) or the minimum (a>0) of our model
Examples of quadratic models are the cinematic equation for position in uniformly accelerated motion
r(t)=r0+v0*t+a*t^2
In which case, for a, meaning acceleration and being a CONSTANT, we find two cases
a<0, which means deacceleration and that we have a maximum (the further position we have)
a>0, possitive acceleration, give us a minimum (the closest position we have)
And so on