Question

a ball is thrown from an initial height of 3 feet with an initial upward veloc
$h = 3 + 21t - 16t^2$
find all values of $t$ for which the balls height is 9 feet.
round your answer(s) to the nearest hundredth.
(if there is more than one answer, use the \or\ button.)

Explanation:

Step1: Set h equal to 9

$9 = 3 + 21t - 16t^2$

Step2: Rearrange to standard quadratic form

$16t^2 - 21t + 6 = 0$

Step3: Apply quadratic formula $t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, $a=16$, $b=-21$, $c=6$
$$t=\frac{21\pm\sqrt{(-21)^2-4(16)(6)}}{2(16)}$$

Step4: Calculate discriminant

$\sqrt{441 - 384}=\sqrt{57}\approx7.55$

Step5: Compute two t values

$t_1=\frac{21+7.55}{32}\approx\frac{28.55}{32}\approx0.89$
$t_2=\frac{21-7.55}{32}\approx\frac{13.45}{32}\approx0.42$

Answer:

$t\approx0.42$ or $t\approx0.89$