Key Concepts
- Nonlinear functions can be used to model business growth, population changes, and physics problems.
- Area and volume based word problems can often be expressed with quadratic equations.
- The volume equation of a rectangle prism is (V = \text{length} \times \text{width} \times \text{height}).
Skills Covered
- Interpreting function values in applied contexts.
- Analyzing nonlinear function models to make predictions.
- Writing an area or a volume equation in terms of one variable.
- Solving for or expressing missing dimensions using quadratic equations.
Example Problems
- A rectangular cutting board has an area of $120 cm²$ and a width of 10 cm. Find its length.
- A stone is thrown from a window. The trajectory of the stone can be represented with the function (h = -5t^2 + 10t + 10), where h is the height of the stone above the ground in meters and t is the second after it is thrown. How many seconds does it take for the stone to reach the ground?
- A box has a length of x inches, a width of (x - 2) inches, and a height of 5 inches. Write a function for its volume.
- A rectangle has an area of 60 cm², and its length is 4 cm more than its width. Find the width.