Question $2$

$(15$ marks$)$

A ball is tossed into the air from a height of $12$ feet at $16$ feet $\frac{?}{sec}.$

$($a$)$ Write the quadratic function that models the height $S($in feet$)$ of the ball as a function of the time $t($in seconds$).$

$($b$)$ How long does it take the ball to reach the ground?

$($c$)$ Calculate the vertex of the function.

$($d$)$ Graph the function $($grid on next page$).$

$($e$)$ Explain the meaning of the coordinates of the vertex for this model.

$($f$)$ Factor $4t^2-4t-3,$ then solve for $t.$

$($g$)$ What do you notice about your answers in part $($b$)$ and in part $($f$)?$ Explain.