b Substitute 3 and 12 for x in the given expression, one at a timek.
C
c Substitute 0 for y in the given expression.
A
aHeight: 80 feet
Explanation: See solution.
B
bHeight After 3 Seconds: 128 feet
Height After 12 of a Second: 108 feet
C
c The ball hit the ground after 5 seconds.
Practice makes perfect
a The following expression describes the height of Perry's ball as a function of time.
y = -16x^2 +64x + 80
Here, y is balls height above ground in feet, and x is the time in second from the moment the ball was thrown. Therefore, the ball was thrown at time x = 0. We can substitute 0 for x in our expression to find the ball's height at the moment of a throw.
The ball was 128 feet above ground 3 seconds after it was thrown. Next, we want to find the ball's height 12 seconds after it was thrown. To do so, we will substitute 12 for x in the given expression.
The ball was 108 feet above ground 12 second after it was thrown.
c When the ball hits the ground, its height above ground is 0 feet. Therefore, to find the time at which the ball hit the ground, we should substitute 0 for y in the given expression.
y = -16x^2 +64x + 80 ⇓ 0 = -16x^2 +64x + 80
We obtained a quadratic equation for x. We will first simplify and factor the above equation.
By the Zero Product Property, if a product of two numbers is 0, then one of these numbers is also equal to 0 .
(x-5)(x+1) = 0 ⇕ x-5=0 or x+1=0
Finally, let's solve the two resulting equations.
x - 5 = 0 ⇔ x = 5
x + 1 = 0 ⇔ x = -1
We have two solutions, x = -1 and x = 5. However, we only care about the positive solution, since we want to find how many second after the ball was thrown did it hit the ground. Therefore, the ball hit the ground after 5 seconds.
