Why It Matters

Find the key features of quadratic, polynomial, and rational functions and use them to solve applications in business

Introduction

[latex]\displaystyle{y}^{{2}}={1}-{x}^{{2}}[/latex]

[latex]\displaystyle{p}={15}-{0.5}{q}[/latex]

[latex]\displaystyle{R}={p}\cdot {q} = {15}{q} -{0.5}{q}^{{2}}[/latex]

[latex]\displaystyle{C}={3p}+{20}[/latex]

[latex]\displaystyle{P}={R}-{C} = {-20} + {12q} - {0.5}^{{2}}[/latex]

Learning Outcomes

• Solve quadratic equations by factoring and quadratic formula
• Find the x and y intercepts and the vertex of a quadratic
• Sketch transformed quadratics
• Determine the equation of a parabola given the vertex and a point, or given the x-intercepts and a point.
• Model revenue as the product of quantity and price from a linear demand function.
• Solve optimization problems involving quadratic functions, including maximizing a quadratic revenue or profit function
• Find the equilibrium price and quantity for quadratic supply/demand curves.
• Evaluate a polynomial function given specific inputs.
• Determine the x and y intercepts of polynomial functions
• Graph a polynomial function using the intercepts and technology
• Determine the x and y intercepts and vertical and horizontal asymptotes of rational functions.

Licenses & Attributions