Question

1. Given that the quadratic function s(t) = at^2+ bt + c represents the distance of a car from Orlando (in miles) after t hours of travel, explain what a, b, and c represent including units.2. A concave up parabola passes through the point (0, 3).From this information, what do you know about the parameters of y = ax^2 + bx + c?

Answer 1

1.

a: acceleration, miles/hour²

b: speed, miles/hour

c: initial distance, miles

2. c = 3

The initial distance is 3 miles

Explanation:

Given the following quadratic function:

`s\left(t\right)=at^2+bt+c`

1.

Where each letter means the following:

a: represents the acceleration, the units would be miles/hour²

b: represents the speed, the units would be miles/hour

c: represents the initial distance, the units would be miles

2.

Now, if we know the point (0, 3), we know the following parameter:

`\begin{gathered} 3=a\cdot0^2+b\cdot0+c \\ \\ c=3 \end{gathered}`

We know the parameter c, that is, the initial distance