Respuesta :
Answer:
2.75 seconds and 133 feet
Step-by-step explanation:
We require to find the coordinates of the vertex of the parabola
the t coordinate ( time ) for a quadratic in standard form is
[tex]t_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
with a = - 16 and b = 88
t = - [tex]\frac{88}{-32}[/tex] = 2.75 seconds ← time taken to reach max
to find the max height evaluate f(2.75 )
f(2.75 ) = - 16( 2.75)² + 88(2.75) + 12 = - 121 + 242 + 12 = 133 feet
The pumpkin reaches the max height of 133 feet and the time taken to reach that height is 2.75 seconds and this can be determined by using the given data.
Given :
The function [tex]\rm f(t) = -16t^2+88t+12[/tex] represents the height (in feet) of a pumpkin t seconds after it is launched from a catapult.
The following steps can be used in order to determine the maximum height and the time to reach:
Step 1 - The formula of the parabola vertex is used in order to determine the time to reach the maximum height.
[tex]\rm t=-\dfrac{b}{2a}[/tex]
Step 2 - Now, substitute the value of 'a' and 'b' in the above formula.
[tex]\rm t=-\dfrac{88}{2\times -16}[/tex]
t = 2.75 sec
Step 3 - Now, substitute the value of t = 2.75 in the expression (1).
[tex]\rm f(2.75) = -16\times(2.75)^2+88\times (2.75)+12[/tex]
Step 4 - Simplify the above expression.
[tex]\rm f(2.75) = -121+242+12 = 133 \;ft[/tex]
For more information, refer to the link given below:
https://brainly.com/question/5245372
