Question

The height of a ball thrown upward from the ground is given by the quadratic function h = 120t - 16t2, where h is in feet and t is in seconds. What is the reasonable range for this function?

Answer 1

A)
[0, 120]
B)
[0, 200]
C)
[0, ∞)
D)
(-∞, ∞)

Answer 2

have you covered parabolas yet?

Answer 3

i dont know .what i have to plug

Answer 4

you may want to cover the parabolas section first I'd think
since this is a parabola

Answer 5

i stiil dont understand i know that iss a parabola . if i use Engineering calculator .what i have to plug .

Answer 6

to solve it usually you'd set it to 0, in this case what you'd want is the vertex of the parabola so \(\bf h = 120t - 16t^2\implies 0={\color{red}{ r}}{\color{red}{ -16}}t^2{\color{blue}{ +120}}t{\color{green}{ +0}}
\\ \quad \\
\textit{vertex of a parabola}\\ \quad \\
y = {\color{red}{ a}}x^2+{\color{blue}{ b}}x+{\color{green}{ c}}\qquad \quad
\left(-\cfrac{{\color{blue}{ b}}}{2{\color{red}{ a}}}\quad ,\quad {\color{green}{ c}}-\cfrac{{\color{blue}{ b}}^2}{4{\color{red}{ a}}}\right)\)

the leading term coefficient is negative, thus it means the parabola is going downwards so notice, the range of the function, that is the values "y" takes, will go from the vertex down