Algebra 2 widens the catalogue of functions. The skill being trained is recognising which family a problem belongs to, because each family has its own standard first move.
Practise quadraticsThree methods solve quadratics: factoring when the roots are rational, completing the square when you need the vertex, and the quadratic formula when nothing else applies. The formula always works, so treat it as the fallback rather than the default.
The discriminant tells you the answer's shape before you compute it. A positive discriminant gives two real roots, zero gives a repeated root, and a negative value gives a complex conjugate pair.
End behaviour is decided by the leading term alone: even degree sends both ends the same way, odd degree sends them opposite ways, and the leading coefficient's sign decides which way.
The factor theorem links roots and factors, if substituting a value gives zero, the corresponding linear expression divides the polynomial. Synthetic division then reduces the degree so you can finish by factoring or by formula.
Rational expressions demand domain awareness: any value making a denominator zero is excluded, even if it cancels during simplification. State those restrictions as part of the answer.
Radical equations can produce extraneous solutions because squaring both sides is not reversible. Every candidate must be substituted back into the original equation before it counts.
Exponential functions change by a constant factor per unit; linear functions change by a constant amount. Growth problems that involve percentages per period are therefore exponential, not linear.
A logarithm answers 'what exponent produces this number?'. That makes logs the tool for solving equations where the unknown sits in an exponent, and the log rules mirror the exponent rules exactly.
