Question

The equation for a projectile's height versus time is h(t)=-16t^2+v^0t+h^o.

A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. What is the maximum height, in feet, the ball will attain?

Round to the nearest whole foot.

Answer 1

\(\bf \text{initial velocity}\\
h = -16t^2+v_ot+h_o \qquad \text{in feet}\\
v_o = \textit{initial speed}\\
h_o = \textit{initial height}\\ \quad \\
\qquad thus\\
h = -16t^2+v_ot+h_o \implies h = -16t^2+(120)t+(2)\ \quad \\\implies h = -16t^2+120t+2\)

notice you have a quadratic equation, and the graph is that one of a parabola, the leading coefficient is negative, thus the parabola is opening downwards,

Answer 2

you can find the vertex of a parabola equation like so, at the coordinates of \(\bf \left(-\cfrac{b}{2a}\quad ,\quad c-\cfrac{b^2}{4a}\right)\)

you're asked to find the maximum height, thus the "y" value at the vertex only, so, you'd only need the y-coordinate

Answer 3

a, b, and c, that is \(\bf y = ax^2+bx+c\)

Answer 4

really dont get any of this.... so whats the answer after putting it all together?

Answer 5

the maximum height, is "y-coordinate" at the vertex
that is the highest point of the parabola