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On a windy morning, a hot air balloon starts rising and flying away from the top of a hill. The altitude, h, in feet, of the balloon x hours after starting its ascent from the hill, can be modeled by the function:
Part A: What is the y-intercept for this function? What does the y-intercept represent in the given situation? Use your equation to explain how you found your answer.
h(x)=-16x2+64x+80

Respuesta :

Answer:

The y-intercept is y = 80feet. The initial height of the balloon is 80feet.

Step-by-step explanation:

[tex]h(x)=-16x^2+64x+80[/tex]

The y-intercept of the function happens when the x-value = 0. So let's plugin x=0 into the function:

[tex]h(x)=-16x^2+64x+80\\h(x)=-16(0)^2+64(0)+80\\h(x)=80[/tex]

The y-intercept is y = 80feet

x represents the number of hours after starting its ascent from the hill, so x = 0hr means when the balloon is just starting to ascent. At the start of the ascent, the balloon has an altitude of 80feet. The initial height of the balloon is 80feet.

The y-intercept is y = 80feet.

The initial height of the balloon is 80feet.

Calculation of the y-intercept and initial height:

Since the equation is [tex]h(x)=-16x^2+64x+80[/tex]

So here x = 0

So

[tex]h(x)=-16(0)^2+64(0)+80[/tex]

= 80

Here, The y-intercept is y = 80feet

Also,

x means the number of hours after starting its ascent from the hill

learn more about intercept here: https://brainly.com/question/15546484

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