Question

The function y=−16x2+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. I need to findthe x-intercept, and when will the apple hit the ground after x seconds.

Answer 1

Answer:

A. x-intercept=x=1.5 , y-intercept=y=36

B.the apple will hit the ground after x=1.5 seconds.

Step-by-step explanation:

A. X-intercept and Y-intercept:

X-intercept:

• the point where the line passes through X-axis i.e. point where y=0

Y-intercept:

• the point where the line passes through Y-axis i.e. point where x=0

Given Equation:

• $y=-16x^2+36$

Finding X-intercept:

to find x-intercept, put y=0 in the given equation as

$0=-16x^2+36$

adding $-16x^2$ to both sides of the equation, we get

$16x^2=36$

dividing both sides by 16, we get

$x^2=\frac{36}{16}\\x^2=2.25$

taking√ on both sides of the equation, we get

$x=\sqrt{2.25}\\ x=1.5$

Finding Y-intercept:

to find y-intercept, put x=0 in the given equation

$y=-16(0)^2+36\\y=36$

thus x-intercept$=x=1.5$

and y-intercept$=y=36$

B.when will the apple hit the ground after x seconds?

In the given equation if x represent the time in seconds then y represents the height of the tree from which the apple is fallen down

so if the apple hits the ground, at this stage the height is zero so y=0, thus we get x as

$0=-16x^2+36$

dividing both sides by 16, we get

$x^2=\frac{36}{16}\\x^2=2.25$

taking√ on both sides of the equation, we get

$x=\sqrt{2.25}\\ x=1.5$

the apple will hit the ground after x=1.5 seconds.