Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Quadratic, rational, and exponential constraints
Construct quadratic rational and exponential constraints with valid contextual domains
Problem types
- Enter a quadratic-model value
- Model with a quadratic
- Equation for an exponential situation
- Build a height model from context, then use it
Builds on
- Solving rational equations
- Building an exponential model
- Solving quadratic equations
- Solving exponential and logarithmic equations · Useful idea
When the unknown is a time or count in an exponent, solving the model equation uses logarithms or equal bases.
- Solving a linear and a nonlinear equation together · Useful idea
The break-even point of a quadratic and a linear model is the solution of a nonlinear system.
- Designs that meet geometric constraints · Earlier idea
The area of a three-sided fenced garden, width times (fence minus two widths), is a quadratic constraint model with a greatest value.
- Modeling with geometry · Earlier idea
Choosing a geometric model of a situation leads to an equation, often quadratic when area is involved.
- Volumes of cylinders, cones, pyramids, spheres · Useful idea
A volume formula in one unknown dimension gives a polynomial equation, often quadratic after a ratio of dimensions is fixed.
- The minimum of an upward-opening quadratic · Useful idea
The vertex of a parabola gives the greatest or least value of a quadratic model, such as maximum height.
- Area and perimeter problems · Earlier idea
Fixing the perimeter of a rectangle makes its area a quadratic function of one side.
Leads to
- Comparing uncertain strategies · See it applied
Finding the best choice often means finding the best value of a model, such as the maximum of a quadratic.
- Checking a model against evidence · See it applied
After solving a quadratic or exponential model, check its solution against the context and the data.
Related skills
- Choosing a periodic model · Related idea
Choosing a model for a situation includes choosing between a quadratic, exponential and sinusoid.
- Completing the square · Shared foundations
- Linear growth against exponential growth · Shared foundations
- Logarithms as inverses of exponentials · Shared foundations
- Graphs of quadratic functions · Shared foundations
Open the interactive map to explore lessons and skill connections.