Alignment to Content Standards
- MATH.CONTENT.HSA.REI.B.4 Solve quadratic equations in one variable.
- MATH.CONTENT. HSF-IF C.8 Interpreting Functions: Analyze functions using different representations.
- MATH.CONTENT.8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Task
The cross section of a hat can be modeled by the following polynomial function:
y=(1/27)(x-15)(x+15) where x and y are measured in cm.
Given these facts, answer the following questions and be sure to show your work:
Note: sketch graph in your work.
- How wide is the hat (not including the bill)? Hint: we are looking for the diameter.
- Measurement of the Crown? Hint: Think of the lowest point in a parabola.
The IM Assessment, IM Assessment Commentary, and solution is attached: