The relationship between time and the height of any ball tossed into the air is always modeled by a quadratic equation.
G
Practice makes perfect
The relationship between time t and the height h of any ball tossed into the air is always modeled by a quadratic equation.
h=at^2+bt+c, a≠0
In order to determine which equation models the relationship for the given ball, we have to find the values of a, b, and c. To do so we will write a system of equations using three of the given points: (0,4), (0.25,10.5), and (0.5,15). Let's start with (0,4).
We now have a system of three equations.
c=4 & (I) 0.0625a+0.25b+c=10.5 & (II) 0.25a+0.5b+c=15 & (III)
Since Equation (I) is already solved for c, we will substitute 4 for c into Equation (II) and Equation (III).
c=4 0.0625a+0.25b+c=10.5 0.25a+0.5b+c=15
(II), (III): c= 4
c=4 0.0625a+0.25b+ 4=10.5 0.25a+0.5b+ 4=15
(II), (III): LHS-4=RHS-4
c=4 0.0625a+0.25b=6.5 0.25a+0.5b=11
Next we will use the Elimination Method. We will start by multiplying both sides of Equation (III) by 0.5. Our goal is to eliminate the b-variable from Equation (II) and solve it for a.
Since we have all three values, we can complete the quadratic equation that models the relationship between time t and the height h of the ball tossed into the air.
h=- 16t^2+30t+4
This corresponds to option G.
