The function y=-16x^{2}+36 represents the height y (in feet) of an apple x

Armorikam

Armorikam

Answered question

2021-09-24

The function y=16x2+36 y (in feet) is the height of an apple x seconds after falling from a tree. Determine the x- and y- intercepts

Answer & Explanation

Layton

Layton

Skilled2021-09-25Added 89 answers

Given: 
The height in y (in feet) of an apple x seconds after falling from a tree given by the function: 
f(x)=16x2+36 ........(1) 
Calculation: 
The x-intercept of the given function is found by setting  to  and solving for f(x)=0 in equation (1), 
f(x)=16x2+36 
0=16x2+36 
16x2=36 
x2=3616 
x2=94 
x=±32 
x=±1.5 
Now, here x stands for time and time cannot be negative, so the solution is x=1.5
Thus, the x-intercept of given function is (1.5, 0). 
The x-intercept in this case provides the time in which apple will hit the ground. 
The y-intercept of the given function is found by substituting x=0 in equation (1), 
f(x)=16x2+36 
y=16(0)2+36 
y=0+36 
y=36 
Thus, the y-intercept of given function is (0,36) 
The y-intercept in this case gives the initial height of the apple.

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