Research and share a realworld problem situation phenomenon

Research and share a real-world problem, situation, phenomenon, or event from that can be modeled using quadratic equations or quadratic inequalities. Post the mathematical model describing your application if available. (If you are a business major, please research a business situation and model to post) You must start a thread before you can read and reply to other threads the value of a new car (in US dollars) is modeled by the quadratic function H(t) = 125 t^2 - 9 3.000t + 22.000. where f represents the number of years since the car was purchased. Calculate and explain what the vertex of this function represents in this context.

Solution

Think of a highway underpass parabolic in shape. If the curve of the underpass can be modeled by h(x) = 100– 0.01x², where x and h(x) are in feet, then how high is the highest point of the underpass, and how wide is it?

Thus, we can find the width and height of underpass using Quadratic equations

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This is a quadratic equation with leading coefficinet postive and hence graph will open UP, thus vertex of the graph represnts the minimum value of the function.

find the vertex as

t = -b/2a

= 3000/(2 *125)

=12

Find value V when t=12 as

V(12)=4000

Thus, vertex is (12, 4000)

Hence after 12 years of purchase Car will have minimum value $4000