Question

At the start of the basketball game, the referee tosses a ball for a jump ball. The equation that models the height of the ball is
h(t) = -16t2 + 24t + 5
During what time interval is the height of the ball above 9 feet?


a) .2 seconds to 1.3 seconds
b) .6 seconds to 1.8 seconds
c) .5 seconds to 2.1 seconds
d) .4 seconds to 1.9 seconds

Answer 1

Let the height/position function equal to 9 and solve for t like a normal quadratic equation. The ball will be above 9 feet between those two t values.

Answer 2

but during what time interval is the height of the ball above 9 feet? (and you have to Round the answer to the nearest tenth of a second.)

Answer 3

The time interval is the interval between the solutions to h(t) = 9.

Answer 4

so which answer choice would best fit this problem?

Answer 5

Put \(h(t) \ge 9\)

\(-16t^2 + 24t + 5 \ge 9 \)
\(-16t^2 + 24t -4 \ge 0 \)
\(4t^2 -6 t +1 \ge 0 \)
Can you solve it?

Answer 6

no -.- i suck in math

Answer 7

Do you know how to solve a quadratic equation?

Answer 8

Sorry, the last line there should be
\(4t^2 -6 t +1 \le 0\) <- solve this

Answer 9

is this right?

Answer 10

Use this formula to solve -> yes
But the range should be like \(x_1\le x \le x_2\) where \(x_1\) and \(x_2\) are the values you get from that formula.

Answer 11

so is it a,b,c, or d ? a) .2 seconds to 1.3 seconds
b) .6 seconds to 1.8 seconds
c) .5 seconds to 2.1 seconds
d) .4 seconds to 1.9 seconds

Answer 12

Can you try to solve it first?

Answer 13

ok

Answer 14

Oh wait this is easy

Answer 15

It's just a quadratic inequality

Answer 16

I dunno how to solve quadratic inequalities :\

Answer 17

me either

Answer 18

Alright... it's like this:
\[\frac{-(-6) -\sqrt{(-6)^2 - 4(4)(1)}}{2(4)} \le x \le \frac{-(-6) -\sqrt{(-6)^2 + 4(4)(1)}}{2(4)} \]
Basically, it's just using the quadratic formula

Answer 19

Simplify it please.

Answer 20

i got d .4 to 1.9 secs ???

Answer 21

Nope, check it again!