a Find the vertex of each parabola. For the values in the table, look for the rows that have the same value in the height column. The vertex should be the midpoint.
B
b Set the first equation equal to the height you want and solve for t. Find the equation of the parabola represented by the table in vertex form, and do the same process.
A
a The projectile represented by the equation goes 28ft higher.
B
bProjectile Represented by the Equation: 0.27 seconds and 3.73 seconds.
Projectile Represented by the Table: 0.38 seconds and 2.62 seconds.
The projectile represented by the equation reached a maximum height of 64ft after 2 seconds. For the second projectile, we are given a table of values where we will highlight the rows with equal heights.
Time (t)
Height (h)
0.5
20
1
32
1.5
36
2
32
From the table above, the vertex must be the midpoint between t=1 and t=2. Therefore, the x-coordinate of the vertex is t=1.5 and its y-coordinate is 36. Let's plot the given data and trace the corresponding parabola.
From the graph, we conclude that the maximum height reached by the projectile represented by the table is 36ft after 1.5 seconds. The greatest height that the projectile represented by a function can reach is equal to 64. This means the projectile represented by a function goes higher by 64-36=28ft.
b To determine when the projectile represented by the equation was at a height of 16ft, we must substitute 16 for the height in the equation h(t) = 64t - 16t^2 and solve it for t.
Therefore, the projectile represented by the equation was at a height of 16ft at t=0.27 seconds and at t=3.73 seconds. For the projectile represented by the table, we must first find its equation. Let's write it in vertex form.
h_2(t) = a(t- h)^2 + k
In this form, the vertex is ( h, k). From Part A we know the vertex is ( 1.5, 36).
h_2(t) = a(t- 1.5)^2 + 36
To find the value of a, we will use the point (0.5,20) from the table. Therefore, h=20 when t=0.5.
We can now write the equation that models the height of the projectile represented by the table.
h_2(t)=-16(t-1.5)^2+36
As before, we must substitute 16 for the height in the above equation.
