Alg 2 — Foundations of Algebra 2 + 5 more topics

Foundations of Algebra 2 typically covers several key areas, reinforcing what you know and expanding on it.

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A quadratic function is any function that can be written in the form:
f(x) = ax² + bx + c
where 'a', 'b', and 'c' are real numbers, and a ≠ 0. The highest power of 'x' is 2.

When you set f(x) = 0, you get a quadratic equation:
ax² + bx + c = 0
The solutions to this equation are called the roots or zeros of the function, and they represent the x-intercepts of the parabola.

Completing the square is a method used to convert a quadratic expression of the form $ax^2 + bx + c$ into the form $a(x-h)^2 + k$. This new form, called vertex form, directly tells you the vertex of the parabola $(h, k)$, which is incredibly helpful for graphing and finding minimum/maximum values.

Let's focus on the case where $a=1$ first, as it's the most common starting point.