Recommended investigations

Altitude to the Hypotenuse: Investigate the relationship between sides of right triangles when an altitude is drawn to the hypotenuse of a right triangle.

Modifying the Slope and Y-Intercept: Examine the changes of a function as the slope and y-intercept of a linear function are modified.

Equation of a Tangent: Find the general equation of a line that touches, but does not pass through, a parabola.

Multiple Solutions: Find the set of solutions of a system of two equations with three variables.

Multiple Inequalities: Identify linear inequalities that determine a predesignated solution.

Coefficients that Affect the Graph: Observe changes in functions as you modify their coefficients.

Moving Parabolas: Generalize the effects on the roots and minimum when modifying a coefficient of a function in the form y = 6x2 + bx.

End Behavior: Examine criteria for producing functions with converging or diverging end behavior.

Intersecting Functions: Explore various cases about the intersections of a linear and quadratic function.

Efficient Fencing: Build a fence that will maximize a region surrounded by a natural boundary.

Arranging Toothpicks: What is the total number of toothpicks used to build a rectangular grid?

Supper with Skiing: Determine the cost of dinner included in a package deal offered by a ski resort.

Gretel's Goldfish: When will Hansel and Gretel have the same number of goldfish?

Bouncing Ball: Determine how high a ball rebounds with each bounce.

Clothes Shopping: Determine which outfit is cheaper in the long run.