Final Answer:
2 seconds
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Explanation:
We are given the height of the volleyball over time:
h = −16t² + 30t + 4
The ball hits the floor when its height h = 0. So we solve:
−16t² + 30t + 4 = 0
This is a quadratic equation in the form at² + bt + c = 0, where:
a = −16, b = 30, c = 4
We use the quadratic formula:
t = [−b ± √(b² − 4ac)] / (2a)
Plug in the numbers:
b² = 30² = 900
4ac = 4 × (−16) × 4 = −256
So b² − 4ac = 900 − (−256) = 900 + 256 = 1156
√1156 = 34 (since 34 × 34 = 1156)
Now compute t:
t = [−30 ± 34] / (2 × −16) = [−30 ± 34] / (−32)
Two possible answers:
1) t = (−30 + 34) / (−32) = 4 / (−32) = −0.125
2) t = (−30 − 34) / (−32) = (−64) / (−32) = 2
Time can’t be negative, so we discard −0.125.
The ball hits the floor after
2 seconds.
Parent Tip: Review the logic above to help your child master the concept of algebra 2 quadratic word problems worksheet.
