Algebra 2 course

1. 1.Quadratic Equations

   A quadratic equation can be written as $ax^2 + bx + c = 0$ with $a \ne 0$. Its graph is a parabola, and the solutions are the $x$-intercepts. There can be two real solutions, one repeated solution, or none, depending on whether the parabola crosses, touches or misses the $x$-axis.

   • Set the equation equal to zero before factoring; the zero-product property needs a zero on one side.
   • Discriminant positive: two real roots; zero: one repeated root; negative: two complex roots.
   • Sum of roots is $-\frac{b}{a}$ and product is $\frac{c}{a}$, a quick check.
   Quick check: What is the larger root of $x^2 - 7x + 12 = 0$?

   $4$

   Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study quadratic equations

2. 2.Logarithms

   A logarithm answers the question: to what power must the base be raised to give this number? So $\log_2 8 = 3$ because $2^3 = 8$. Logarithms undo exponentials, which is why they appear whenever the unknown sits in an exponent, as in compound interest, population growth, pH and decibels.

   • $\log_b(xy) = \log_b x + \log_b y$ and $\log_b \frac{x}{y} = \log_b x - \log_b y$.
   • $\log_b(x^k) = k \log_b x$, the rule that brings an exponent down.
   • Logs are defined only for positive arguments; check solutions against the domain.
   Quick check: Evaluate $\log_3 81$.

   $4$

   Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study logarithms

These topics belong to the course outline. Full explainers for them have not been written yet, so they are summarised here rather than given pages of their own.

Rational Expressions

Simplify, multiply, divide, add and subtract fractions of polynomials; note excluded values.

Exponents and Radicals

Rational exponents and simplifying radicals.

Absolute Value Equations

Split |A| = B into A = B and A = -B, and check that B is not negative.

• Algebra 1
• Algebra overview
• All subjects