To use the quadratic formula, we first need to put the equation in standard form:
𝑦 = −5𝑥^2 + 20𝑥 + 0.05
𝑦 = -5(𝑥^2 - 4𝑥) + 0.05
𝑦 = -5(𝑥^2 - 4𝑥 + 4) + 20 + 0.05
𝑦 = -5(𝑥 - 2)^2 + 20.05
Now we can see that the vertex of the parabola is at (2, 20.05), which represents the maximum height of the ball.
To find how long the ball is in the air, we need to find the x-intercepts of the parabola. This represents when the ball hits the ground.
𝑦 = −5𝑥^2 + 20𝑥 + 0.05 = 0
Using the quadratic formula:
𝑥 = (−20 ± √(20^2 − 4(−5)(0.05)))/(2(−5))
Simplifying:
𝑥 = (−20 ± √402.05))/(-10)
𝑥 ≈ 0.04 or 𝑥 ≈ 3.96
Since we are only interested in the time that the ball is in the air, we can ignore the solution of 𝑥 ≈ 0.04 (which represents when the ball is initially hit from the tee).
Therefore, the ball is in the air for approximately 3.96 seconds before it hits the ground.
A golf ball is hit from the top of a tee. The quadratic equation
𝑦 = −5𝑥2 + 20𝑥 + 0.05 describes its height, 𝑦, in meters as time, 𝑥, in seconds
passes. Determine how long the ball is in the air
Use the quadratic formula.
1 answer