Question

Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?

1.3 ft

2.6 ft

26.0 ft

27.6 ft


This is C right?

Answer 1

have you covered parabolas yet?

Answer 2

Yes but I dont understand them

Answer 3

@TwinYang

Answer 4

well \(\bf \text{initial velocity}\\
h = -16t^2+v_ot+h_o \qquad \text{in feet}\\

\\ \quad \\

v_o=\textit{initial velocity of the object}\to 42\\
h_o=\textit{initial height of the object, from the ground}\to 0\\
h=\textit{height of the object at "t" seconds}
\\ \quad \\
h = -16t^2+v_ot+h_o\implies h = -16t^2+{\color{brown}{ 42}}t+{\color{brown}{ 0}}
\\ \quad \\
\implies h=-16t^2+42t\)

notice is a quadratic equation, and thus is a parabola graph, the leading term coefficient is negative, meaning the parabola is going downwards, thus
thus

so the "ball" gets to its highest at the vertex of the parabola
\(\bf \textit{vertex of a parabola}\\ \quad \\
y = {\color{red}{ a}}x^2+{\color{blue}{ b}}x+{\color{green}{ c}}\qquad


\left(-\cfrac{{\color{blue}{ b}}}{2{\color{red}{ a}}}\quad ,\quad {\color{green}{ c}}-\cfrac{{\color{blue}{ b}}^2}{4{\color{red}{ a}}}\right)\)