Question

The function y=16x squared + 36 represents the height y (in feet) of an apple x seconds after falling from a tree. Find and interpret the x- and y-intercepts.

Answer 1

y = 16x^2 + 36
Lets find the intercepts, making x and y to zero and solving:
0 = 16x^2 + 36
16x^2 = -36
therefore there is not x-intercept, that is, when y equals zero the function does not have a value, is not defined.
Now, the y intercept, that is when x equals zero:
y = 16x^2 + 36
y = 16(0)^2 + 36
y = 36
so, when x = 0, y = 36, that is, the function hits the y axis when x = 0

Answer 2

ok so if we were to do the equation in real life, then it is not true since accorind to the equation, the apple goes higher as the time passses, therefor I conclude you forgot to include a (-) sign in front of the 16x^2 so therefor the true equation is y=-16x^2+36

x intercept is when the graph crosses the x axis or when y=0
y intercept is when the graph crosses the y axis or when x=0

so x intercept
y=-16x^2+36
y=0
0=-16x^2+36
add 16x^2 to both sides
16x^2=36
divide both sides by 4
4x^2=9
divide both sides by 4
x^2=9/4
therefor
x=-3/2 or 3/2
since x represents time and you cannot have negative time in real life, discard -3/2
x intercept=3/2 (times=3/2 seconds ie, the apple hits the ground at 3/2 seconds)

y intercept
set x=0
y=-16(0)^2+36
y=36
y intercept=36 (this is the starting height of the apple)


x intercept=3/2
y intercept=36