Once you know the parent function, you can sketch any transformation by reading the equation. Master the four moves — vertical/horizontal shift, reflection, stretch — and you'll graph every quadratic, root, and absolute-value function on sight.

An inverse function undoes the original. Swap x and y, solve for y — that's the whole technique. Plus the geometric meaning (reflection across y = x) and the horizontal-line test for invertibility.

Algebra 1 introduced parabolas. Algebra 2 makes you fluent — switch between forms, complete the square in your head, and read the discriminant to know exactly how many real roots before solving.

The imaginary unit i = √(−1) extends the number line into a plane. Master arithmetic with complex numbers, the conjugate trick for division, and you will handle every "no real solution" quadratic on the CBE.

Four parent functions, four shapes, four sets of rules. Domain restrictions for square roots, the symmetry of cube roots, the V of absolute value, and how transformations apply uniformly to all of them.

Algebra 1 introduced exponential growth. Algebra 2 deepens it: the natural base e, continuous compounding, and decay problems where the half-life is measured in years.

<p>What is the minimum degree of a polynomial whose graph looks like this?</p>

<p>Identify the function that has VA at x = 0 only.</p>

<p>Identify the conic: its branches open up and down.</p>