$x^2$Algebra 2

Shifting and Stretching Graphs

Learn a handful of parent graphs, then move any of them anywhere with y = a·f(x − h) + k. Combine functions, chain them together, and run them backwards with inverses.

Matrices Move the Plane

Solve three equations in three unknowns, then meet matrices: grids of numbers that rotate, stretch and squash the whole plane. The determinant turns out to be an area.

When the Parabola Misses

Three forms of a quadratic and what each one tells you, completing the square, and what happens when a parabola never touches the axis: the invention of i, the number whose square is −1.

The Shape of Polynomials

Read a polynomial's graph from its degree and leading coefficient, see how repeated roots bounce instead of cross, divide polynomials with a shortcut, and count roots with the Fundamental Theorem of Algebra.

Asymptotes and Holes

Rational functions have walls they never cross and holes you cannot see. Move asymptotes around, find holes by cancelling, solve rational equations without falling into the extraneous trap, and meet inverse variation.

Fractional Powers

What could x to the power one half mean? Discover that roots ARE powers, simplify with the exponent rules you already know, and solve radical equations while dodging fake solutions.

Logarithms Undo Powers

Exponential growth, the strange number e, and logarithms: the question "what power?". Use them to solve for time in a savings account, and see why earthquake and sound scales use logs.

Patterns That Add Up

Arithmetic sequences add, geometric ones multiply. Add a hundred numbers in your head like young Gauss, watch infinitely many numbers add up to something finite, and settle Zeno's paradox.

Slicing a Cone

Slice a double cone at different angles and you get a circle, an ellipse, a parabola or a hyperbola. Draw each one, read its equation, and find out why whispers travel across some rooms.

Counting Chances

Count outcomes cleverly with permutations and combinations, compute conditional probability, check predictions with a simulator, and meet the bell curve that describes heights, test scores and errors.