Question

the table shows the approximate height of a projectile x seconds after being fired into the air. which equation models the height, y, x seconds after firing? projectile motion

time (seconds)	height (meters)
0	0
1	40
2	60
3	60
4	40
5	0

o y = -10(x)(x - 5)
o y = 10(x)(x - 5)
o y = -10(x - 5)
o y = 10(x - 5)

Explanation:

Step1: Check x = 0

Substitute \(x = 0\) into each equation.
For \(y=-10(x)(x - 5)\), when \(x = 0\), \(y=-10\times0\times(0 - 5)=0\).
For \(y = 10(x)(x - 5)\), when \(x = 0\), \(y=10\times0\times(0 - 5)=0\).
For \(y=-10(x - 5)\), when \(x = 0\), \(y=-10\times(0 - 5)=50\).
For \(y = 10(x - 5)\), when \(x = 0\), \(y=10\times(0 - 5)=- 50\). So we can rule out the last two - equations since when \(x = 0\), \(y = 0\) in the table.

Step2: Check x = 1

For \(y=-10(x)(x - 5)\), when \(x = 1\), \(y=-10\times1\times(1 - 5)=-10\times(-4)=40\).
For \(y = 10(x)(x - 5)\), when \(x = 1\), \(y=10\times1\times(1 - 5)=10\times(-4)=-40\).

Answer:

\(y=-10(x)(x - 5)\)