8.8B Homework Writing & Analyzing Real-World Quadratic Functions

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4 questions

The quarterbacks on the high school football team want to see who can get the most hang time when throwing the ball. Connor knows that using his initial velocity and height, he can model the trajectory of his throw with the equation {𝒉=−𝟏𝟔𝒕^𝟐+𝟗𝟓𝒕+𝟓.𝟐}, where 𝒉 is the height of the ball in feet and 𝒕 is the time in seconds after throwing.
Round all values to one decimal place.

{\bold a)} vertex {(t,h)} _______ 
      y-intercept {(t,h)} _______ 

{\bold b)} What is the maximum height of the ball?
      about _______feet

{\bold c)} After how many seconds did the ball reach the maximum height?
      about _______seconds

{\bold d)} Approximately how long was the ball in the air?
      about _______seconds
{\bold e)} Which feature of the function/graph represents the height of the ball in feet when Connor threw it?
_______ 

The normal blood pressure of an adult woman 𝑷 in millimeters of mercury given her age 𝒕 in years can be modeled by the equation below and shown on the graph to the right.
{𝑷=𝟎.𝟎𝟏𝒕^𝟐+𝟎.𝟓𝒕+𝟏𝟎𝟕}
{\bold a)} If Seiko’s blood pressure is 126, about how old would she be according to the graph? _______yrs old
{\bold b)} Substitute your answer to part (a) into the equation to check your answer. _______ 
{\bold c)} Notice that the y-intercept is not shown on the graph. What is the y-intercept? _______ 
{\bold d)} What would be the age of a person with this blood pressure? _______ 

You throw a ball to your dog. The function graphed at the right represents the path of the ball, where 𝒙 is the horizontal distance (in feet) and 𝒚 is the height (in feet).

{\bold a)} Write a quadratic equation in vertex form to model this scenario.
    {y=}_______ 

{\bold b)} When was the ball increasing in height?
    _______feet {\lt x \lt}_______feet 

{\bold c)} Your dog jumps up to catch the ball, as shown on the graph. How high is the ball when your dog catches it?
     _______feet

{\bold d)} What is the y-intercept?
     _______feet

e) What is the domain and range of this function in the given context?
     _______feet {\lt x \lt}_______feet
     _______feet {\lt y \lt}_______feet

2A flare is launched from a boat and travels in a parabolic path until reaching the water with a maximum height of 300 feet, represented by a vertex of (59, 300), landing in the water at the point (119, 0).

{\bold a)} Write a quadratic function in vertex form that models the path of the flare.
f(x)=_______

{\bold b)} What was the initial height of the flare? (to the nearest tenth of a foot)
_______feet