Advanced Math
Quadratics, exponentials, and function transformations. Taught with Desmos strategies so you solve them faster than by hand.
Equivalent Expressions
Safe numbers only. Always set sliders to numbers other than 0 or 1.
The visual proof of equivalence is when one graph is directly on top of the other across all visible points.
Change your slider value to a second safe number to confirm the overlap is not a coincidence.
"Is equivalent to" in the prompt means use the graphing strategy first.
Nonlinear Equations
Vertex form for min/max: always use y = a(x - h)^2 + k when a problem mentions the highest or lowest point.
Graphing beats regression for multiple solutions: visualize intersections, do not rely on the tilde symbol.
Area is scale factor squared. Volume is scale factor cubed.
Verify R^2 = 1 to confirm your regression model perfectly fits the data.
Nonlinear Functions
Vertex form mastery: always use y = a(x - h)^2 + k for any highest or lowest point problem.
Graphing over regression: for counting or summing solutions, visualize intersections on the graph.
Safe sliders: never use 0 or 1 for constant sliders when checking equivalent expressions.
Check R^2: a valid regression model for SAT data must have R^2 = 1.