8.8B Homework Writing & Analyzing Real-World Quadratic Functions

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