The height of the ball after 3 seconds in air is 219 feet
Step-by-step explanation:
The form of the quadratic function is f(x) = ax² + bx + c, where
- a is the coefficient of x²
- b is the coefficient of x
- c is the numerical term (value f at x = 0)
∵ h(x) represents the height of the ball in the air after x seconds
∵ h(x) is a quadratic function
∴ h(x) = ax² + bx + c
- The value of c is zero because h(x) represents the height of
the ball in air, then the initial height is 0
∴ h(x) = ax² + bx
∵ The height of the ball after 1 second is 91 feet
∴ x = 1 and y = 91
∴ 91 = a(1)² + b(1)
∴ 91 = a + b
- Switch the two sides
∴ a + b = 91 ⇒ (1)
∵ The height of the ball after 2 second is 164 feet
∴ x = 2 and y = 164
∴ 164 = a(2)² + b(2)
∴ 164 = 4a + 2b
- Switch the two sides
∴ 4a + 2b = 164
- Divide all terms by 2
∴ 2a + b = 82 ⇒ (2)
Now we have a system of equations to solve it
Subtract equation (1) from (2) to eliminate b
∴ a = -9
- Substitute the value of a in equation (1) to find b
∵ -9 + b = 91
- Add 9 to both sides
∴ b = 100
- Substitute a and b in h(x)
∴ h(x) = -9x² + 100x
∵ x = 3 seconds
∴ h(3) = -9(3)² + 100(3)
∴ h(3) = -81 + 300
∴ h(3) = 219 feet
The height of the ball after 3 seconds in air is 219 feet
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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