The range of the function is from 2 feet to 12.25 feet
Step-by-step explanation:
In a function f(x) = y
- x is the domain of the function
- y is the range of the function
The height (h) of the ball at time (t) seconds can be represented by the equation h(t) = - 16 t² + 20 t + 6
∵ h(t) = - 16 t² + 20 t + 6
∴ The domain is t
∴ The range is h(t)
- To find the range of the quadratic function find the maximum or
minimum value of it
∵ The leading coefficient of the function is -16
∴ The function has a maximum value
To find the maximum value differentiate h(t) with respect to t and equate it by 0 to find the value of t for the maximum height
∵ h'(t) = -16(2) t + 20(1)
∴ h'(t) = -32 t + 20
- Equate it by 0
∵ h'(t) = 0
∴ -32 t + 20 = 0
- Subtract 20 from both sides
∴ -32 t = - 20
- Divide both sides by -32
∴ t = 0.625 seconds ⇒ time for the maximum height
Substitute the value of t in h(t) to find the maximum height
∵ h(0.625) = -16(0.625)² + 20(0.625) + 6
∴ h(t) = 12.25 feet
∴ The maximum height of the ball is 12.25 feet
∵ The ball is caught at 2 feet
∴ The range of the function is 2 ≤ h(t) ≤ 12.25
The range of the function is from 2 feet to 12.25 feet
Learn more:
You can learn more about the quadratic equations in brainly.com/question/9390381
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