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 h(x)=−16x2+64x+80
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 h(x)=−16x2+64x+80{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>-</mo><mn>16</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>64</mn><mi>x</mi><mo>+</mo><mn>80</mn></math>"}.
Part A: What is the value of 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.
Part B: There is a positive and negative x-intercept for this function. What is the positive x-intercept value? Explain what this x-intercept represents in this given situation. Show your work.
Part C: What is the maximum height, in feet, the balloon will reach? Show your work.
Part D: After how many hours will the balloon reach its maximum height?
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