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Solving a problem involving a quadratic (or second-degree polynomial) function requires understanding all the properties of a quadratic function and knowing how to solve an equation out of context. Consult the following concept sheet if needed: Solving a Second-degree Equation or Inequality.
The kinetic energy of an object, denoted |E_k,| is the energy that an object possesses due to its motion. The formula for calculating the kinetic energy of an object as a function of its speed is a quadratic function. ||\begin{align} E_k = \frac{1}{2}&mv^2 \\\\ \text{where} \quad E_k &: \text{kinetic energy (J)}\\ m\ &: \text{mass of the object (kg)} \\ v\ \ &: \text{speed of the object (m/s)}\end{align}||
a) What is the kinetic energy of a tennis ball that weighs |58| grams and moves at a speed of |198\ \text{km/h}|?
b) What is the speed in |\text{km/h}| of a golf ball weighing |44| grams if it has the same kinetic energy as the tennis ball in question a)?
A stock listed on the stock exchange reaches a minimum value of |\$ 4.00| six months after being listed on the stock exchange. The function that represents the decrease in the value of the stock during the first six months after being listed is a quadratic function.
a) If the stock was valued at |\$ 6.00| when it was first listed, what is its value four months later?
b) At what point in the first six months did the stock reach a value of |\$ 5.00|?
In the previous example, there were only equations and not inequalities. A final question using inequalities could be: "During what time interval was the stock's value less than |\$ 5.00|?"
To find out how to solve this kind of question, consult the following concept sheet: Solving a Single-variable Second-degree Polynomial Inequality.
The amount of water in the tank of a wastewater treatment plant varies depending on the time of day. This situation can be modeled using a quadratic function. The plant's tank is filled to its capacity of |25\ 000\ \text{L}| at noon. It is empty at 8 p.m (20:00).
a) What is the equation in standard form associated with the amount of water in the reservoir depending on the time of day?
b) At what times is the factory tank filled with |15\ 000\ \text{L}|?